1.6 Rational Expressions - College Algebra 2e | OpenStax (2024)

Table of Contents
Learning Objectives Simplifying Rational Expressions How To Example 1 Simplifying Rational Expressions Solution Analysis Q&A Try It #1 Multiplying Rational Expressions How To Example 2 Multiplying Rational Expressions Solution Try It #2 Dividing Rational Expressions How To Example 3 Dividing Rational Expressions Solution Try It #3 Adding and Subtracting Rational Expressions How To Example 4 Adding Rational Expressions Solution Analysis Example 5 Subtracting Rational Expressions Solution Q&A Try It #4 Simplifying Complex Rational Expressions How To Example 6 Simplifying Complex Rational Expressions Solution Try It #5 Q&A Media 1.6 Section Exercises Verbal Algebraic Real-World Applications Extensions FAQs

Learning Objectives

In this section, you will:

  • Simplify rational expressions.
  • Multiply rational expressions.
  • Divide rational expressions.
  • Add and subtract rational expressions.
  • Simplify complex rational expressions.

A pastry shop has fixed costs of $280 $280 per week and variable costs of $9 $9 per box of pastries. The shop’s costs per week in terms of x, x, the number of boxes made, is 280+9x. 280+9x. We can divide the costs per week by the number of boxes made to determine the cost per box of pastries.

280+9x x 280+9x x

Notice that the result is a polynomial expression divided by a second polynomial expression. In this section, we will explore quotients of polynomial expressions.

Simplifying Rational Expressions

The quotient of two polynomial expressions is called a rational expression. We can apply the properties of fractions to rational expressions, such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator. Let’s start with the rational expression shown.

x 2 +8x+16 x 2 +11x+28 x 2 +8x+16 x 2 +11x+28

We can factor the numerator and denominator to rewrite the expression.

(x+4) 2 (x+4)(x+7) (x+4) 2 (x+4)(x+7)

Then we can simplify that expression by canceling the common factor ( x+4 ). ( x+4 ).

x+4 x+7 x+4 x+7

How To

Given a rational expression, simplify it.

  1. Factor the numerator and denominator.
  2. Cancel any common factors.

Example 1

Simplifying Rational Expressions

Simplify x 2 −9 x 2 +4x+3 . x 2 −9 x 2 +4x+3 .

Solution

(x+3)(x−3) (x+3)(x+1) Factorthenumeratorandthedenominator. x−3 x+1 Cancelcommonfactor(x+3). (x+3)(x−3) (x+3)(x+1) Factorthenumeratorandthedenominator. x−3 x+1 Cancelcommonfactor(x+3).

Analysis

We can cancel the common factor because any expression divided by itself is equal to 1.

Q&A

Can the x 2 x 2 term be cancelled in Example 1?

No. A factor is an expression that is multiplied by another expression. The x 2 x 2 term is not a factor of the numerator or the denominator.

Try It #1

Simplify x−6 x 2 −36 . x−6 x 2 −36 .

Multiplying Rational Expressions

Multiplication of rational expressions works the same way as multiplication of any other fractions. We multiply the numerators to find the numerator of the product, and then multiply the denominators to find the denominator of the product. Before multiplying, it is helpful to factor the numerators and denominators just as we did when simplifying rational expressions. We are often able to simplify the product of rational expressions.

How To

Given two rational expressions, multiply them.

  1. Factor the numerator and denominator.
  2. Multiply the numerators.
  3. Multiply the denominators.
  4. Simplify.

Example 2

Multiplying Rational Expressions

Multiply the rational expressions and show the product in simplest form:

x2+4x−53x+18⋅2x−1x+5x2+4x−53x+18⋅2x−1x+5

Solution

(x+5)(x−1) 3(x+6) ⋅ (2x−1) (x+5) Factorthenumeratoranddenominator. (x+5)(x−1)(2x−1) 3(x+6)(x+5) Multiplynumeratorsanddenominators. (x+5) (x−1)(2x−1) 3(x+6) (x+5) Cancelcommonfactorstosimplify. (x−1)(2x−1) 3(x+6) (x+5)(x−1) 3(x+6) ⋅ (2x−1) (x+5) Factorthenumeratoranddenominator. (x+5)(x−1)(2x−1) 3(x+6)(x+5) Multiplynumeratorsanddenominators. (x+5) (x−1)(2x−1) 3(x+6) (x+5) Cancelcommonfactorstosimplify. (x−1)(2x−1) 3(x+6)

Try It #2

Multiply the rational expressions and show the product in simplest form:

x 2 +11x+30 x 2 +5x+6 ⋅ x 2 +7x+12 x 2 +8x+16 x 2 +11x+30 x 2 +5x+6 ⋅ x 2 +7x+12 x 2 +8x+16

Dividing Rational Expressions

Division of rational expressions works the same way as division of other fractions. To divide a rational expression by another rational expression, multiply the first expression by the reciprocal of the second. Using this approach, we would rewrite 1 x ÷ x 2 3 1 x ÷ x 2 3 as the product 1 x ⋅ 3 x 2 . 1 x ⋅ 3 x 2 . Once the division expression has been rewritten as a multiplication expression, we can multiply as we did before.

1 x ⋅ 3 x 2 = 3 x 3 1 x ⋅ 3 x 2 = 3 x 3

How To

Given two rational expressions, divide them.

  1. Rewrite as the first rational expression multiplied by the reciprocal of the second.
  2. Factor the numerators and denominators.
  3. Multiply the numerators.
  4. Multiply the denominators.
  5. Simplify.

Example 3

Dividing Rational Expressions

Divide the rational expressions and express the quotient in simplest form:

2 x 2 +x−6 x 2 −1 ÷ x 2 −4 x 2 +2x+1 2 x 2 +x−6 x 2 −1 ÷ x 2 −4 x 2 +2x+1

Solution

2x2+x−6x2−1⋅x2+2x+1x2−4Rewrite as multiplication.(2x−3)(x+2)(x+1)(x−1)⋅(x+1)2(x+2)(x−2)Factor.(2x−3)(x+2)(x+1)2(x+1)(x−1)(x+2)(x−2)Multiply.(2x−3)(x+1)(x−1)(x−2)Cancel common factors to simplify.2x2+x−6x2−1⋅x2+2x+1x2−4Rewrite as multiplication.(2x−3)(x+2)(x+1)(x−1)⋅(x+1)2(x+2)(x−2)Factor.(2x−3)(x+2)(x+1)2(x+1)(x−1)(x+2)(x−2)Multiply.(2x−3)(x+1)(x−1)(x−2)Cancel common factors to simplify.

Try It #3

Divide the rational expressions and express the quotient in simplest form:

9 x 2 −16 3 x 2 +17x−28 ÷ 3 x 2 −2x−8 x 2 +5x−14 9 x 2 −16 3 x 2 +17x−28 ÷ 3 x 2 −2x−8 x 2 +5x−14

Adding and Subtracting Rational Expressions

Adding and subtracting rational expressions works just like adding and subtracting numerical fractions. To add fractions, we need to find a common denominator. Let’s look at an example of fraction addition.

5 24 + 1 40 = 25 120 + 3 120 = 28 120 = 7 30 5 24 + 1 40 = 25 120 + 3 120 = 28 120 = 7 30

We have to rewrite the fractions so they share a common denominator before we are able to add. We must do the same thing when adding or subtracting rational expressions.

The easiest common denominator to use will be the least common denominator, or LCD. The LCD is the smallest multiple that the denominators have in common. To find the LCD of two rational expressions, we factor the expressions and multiply all of the distinct factors. For instance, if the factored denominators were (x+3)(x+4) (x+3)(x+4) and (x+4)(x+5), (x+4)(x+5), then the LCD would be (x+3)(x+4)(x+5). (x+3)(x+4)(x+5).

Once we find the LCD, we need to multiply each expression by the form of 1 that will change the denominator to the LCD. We would need to multiply the expression with a denominator of (x+3)(x+4) (x+3)(x+4) by x+5 x+5 x+5 x+5 and the expression with a denominator of (x+4)(x+5) (x+4)(x+5) by x+3 x+3 . x+3 x+3 .

How To

Given two rational expressions, add or subtract them.

  1. Factor the numerator and denominator.
  2. Find the LCD of the expressions.
  3. Multiply the expressions by a form of 1 that changes the denominators to the LCD.
  4. Add or subtract the numerators.
  5. Simplify.

Example 4

Adding Rational Expressions

Add the rational expressions:

5 x + 6 y 5 x + 6 y

Solution

First, we have to find the LCD. In this case, the LCD will be xy. xy. We then multiply each expression by the appropriate form of 1 to obtain xy xy as the denominator for each fraction.

5 x ⋅ y y + 6 y ⋅ x x 5y xy + 6x xy 5 x ⋅ y y + 6 y ⋅ x x 5y xy + 6x xy

Now that the expressions have the same denominator, we simply add the numerators to find the sum.

See Also
Factors of 420? How to Find the Factors of 420 by Prime Factorization Method?Applied Analysis in Biological and Physical Sciences [electronic resource] : ICMBAA, Aligarh, India, June 2015 / edited by Jim M. Cushing, M. Saleem, H. M. Srivastava, Mumtaz Ahmad Khan, M. MerajuddinRemainder Calculatormathematics in history and culture in SearchWorks catalog

6x+5y xy 6x+5y xy

Analysis

Multiplying by y y y y or x x x x does not change the value of the original expression because any number divided by itself is 1, and multiplying an expression by 1 gives the original expression.

Example 5

Subtracting Rational Expressions

Subtract the rational expressions:

6 x 2 +4x+4 − 2 x 2 −4 6 x 2 +4x+4 − 2 x 2 −4

Solution

6 (x+2) 2 − 2 (x+2)(x−2) Factor. 6 (x+2) 2 ⋅ x−2 x−2 − 2 (x+2)(x−2) ⋅ x+2 x+2 MultiplyeachfractiontogetLCDasdenominator. 6(x−2) (x+2) 2 (x−2) − 2(x+2) (x+2) 2 (x−2) Multiply. 6x−12−(2x+4) (x+2) 2 (x−2) Applydistributiveproperty. 4x−16 (x+2) 2 (x−2) Subtract. 4(x−4) (x+2) 2 (x−2) Simplify. 6 (x+2) 2 − 2 (x+2)(x−2) Factor. 6 (x+2) 2 ⋅ x−2 x−2 − 2 (x+2)(x−2) ⋅ x+2 x+2 MultiplyeachfractiontogetLCDasdenominator. 6(x−2) (x+2) 2 (x−2) − 2(x+2) (x+2) 2 (x−2) Multiply. 6x−12−(2x+4) (x+2) 2 (x−2) Applydistributiveproperty. 4x−16 (x+2) 2 (x−2) Subtract. 4(x−4) (x+2) 2 (x−2) Simplify.

Q&A

Do we have to use the LCD to add or subtract rational expressions?

No. Any common denominator will work, but it is easiest to use the LCD.

Try It #4

Subtract the rational expressions: 3 x+5 − 1 x−3 . 3 x+5 − 1 x−3 .

Simplifying Complex Rational Expressions

A complex rational expression is a rational expression that contains additional rational expressions in the numerator, the denominator, or both. We can simplify complex rational expressions by rewriting the numerator and denominator as single rational expressions and dividing. The complex rational expression a 1 b +c a 1 b +c can be simplified by rewriting the numerator as the fraction a 1 a 1 and combining the expressions in the denominator as 1+bc b . 1+bc b . We can then rewrite the expression as a multiplication problem using the reciprocal of the denominator. We get a 1 ⋅ b 1+bc , a 1 ⋅ b 1+bc , which is equal to ab 1+bc . ab 1+bc .

How To

Given a complex rational expression, simplify it.

  1. Combine the expressions in the numerator into a single rational expression by adding or subtracting.
  2. Combine the expressions in the denominator into a single rational expression by adding or subtracting.
  3. Rewrite as the numerator divided by the denominator.
  4. Rewrite as multiplication.
  5. Multiply.
  6. Simplify.

Example 6

Simplifying Complex Rational Expressions

Simplify: y+ 1 x x y y+ 1 x x y .

Solution

Begin by combining the expressions in the numerator into one expression.

y⋅xx+1x   MultiplybyxxtogetLCDasdenominator. xyx+1x xy+1x   Addnumerators. y⋅xx+1x   MultiplybyxxtogetLCDasdenominator. xyx+1x xy+1x   Addnumerators.

Now the numerator is a single rational expression and the denominator is a single rational expression.

xy+1 x x y xy+1 x x y

We can rewrite this as division, and then multiplication.

xy+1 x ÷ x y xy+1 x ⋅ y x Rewriteasmultiplication. y(xy+1) x 2 Multiply. xy+1 x ÷ x y xy+1 x ⋅ y x Rewriteasmultiplication. y(xy+1) x 2 Multiply.

Try It #5

Simplify: x y − y x y x y − y x y

Q&A

Can a complex rational expression always be simplified?

Yes. We can always rewrite a complex rational expression as a simplified rational expression.

Media

Access these online resources for additional instruction and practice with rational expressions.

  • Simplify Rational Expressions
  • Multiply and Divide Rational Expressions
  • Add and Subtract Rational Expressions
  • Simplify a Complex Fraction

1.6 Section Exercises

Verbal

1.

How can you use factoring to simplify rational expressions?

2.

How do you use the LCD to combine two rational expressions?

3.

Tell whether the following statement is true or false and explain why: You only need to find the LCD when adding or subtracting rational expressions.

Algebraic

For the following exercises, simplify the rational expressions.

4.

x 2 −16 x 2 −5x+4 x 2 −16 x 2 −5x+4

5.

y 2 +10y+25 y 2 +11y+30 y 2 +10y+25 y 2 +11y+30

6.

6 a 2 −24a+24 6 a 2 −24 6 a 2 −24a+24 6 a 2 −24

7.

9 b 2 +18b+9 3b+3 9 b 2 +18b+9 3b+3

8.

m−12 m 2 −144 m−12 m 2 −144

9.

2 x 2 +7x−4 4 x 2 +2x−2 2 x 2 +7x−4 4 x 2 +2x−2

10.

6 x 2 +5x−4 3 x 2 +19x+20 6 x 2 +5x−4 3 x 2 +19x+20

12.

3 c 2 +25c−18 3 c 2 −23c+14 3 c 2 +25c−18 3 c 2 −23c+14

13.

12 n 2 −29n−8 28 n 2 −5n−3 12 n 2 −29n−8 28 n 2 −5n−3

For the following exercises, multiply the rational expressions and express the product in simplest form.

14.

x 2 −x−6 2 x 2 +x−6 ⋅ 2 x 2 +7x−15 x 2 −9 x 2 −x−6 2 x 2 +x−6 ⋅ 2 x 2 +7x−15 x 2 −9

15.

c 2 +2c−24 c 2 +12c+36 ⋅ c 2 −10c+24 c 2 −8c+16 c 2 +2c−24 c 2 +12c+36 ⋅ c 2 −10c+24 c 2 −8c+16

16.

2 d 2 +9d−35 d 2 +10d+21 ⋅ 3 d 2 +2d−21 3 d 2 +14d−49 2 d 2 +9d−35 d 2 +10d+21 ⋅ 3 d 2 +2d−21 3 d 2 +14d−49

17.

10 h 2 −9h−9 2 h 2 −19h+24 ⋅ h 2 −16h+64 5 h 2 −37h−24 10 h 2 −9h−9 2 h 2 −19h+24 ⋅ h 2 −16h+64 5 h 2 −37h−24

18.

6 b 2 +13b+6 4 b 2 −9 ⋅ 6 b 2 +31b−30 18 b 2 −3b−10 6 b 2 +13b+6 4 b 2 −9 ⋅ 6 b 2 +31b−30 18 b 2 −3b−10

19.

2 d 2 +15d+25 4 d 2 −25 ⋅ 2 d 2 −15d+25 25 d 2 −1 2 d 2 +15d+25 4 d 2 −25 ⋅ 2 d 2 −15d+25 25 d 2 −1

20.

6 x 2 −5x−50 15 x 2 −44x−20 ⋅ 20 x 2 −7x−6 2 x 2 +9x+10 6 x 2 −5x−50 15 x 2 −44x−20 ⋅ 20 x 2 −7x−6 2 x 2 +9x+10

21.

t 2 −1 t 2 +4t+3 ⋅ t 2 +2t−15 t 2 −4t+3 t 2 −1 t 2 +4t+3 ⋅ t 2 +2t−15 t 2 −4t+3

22.

2 n 2 −n−15 6 n 2 +13n−5 ⋅ 12 n 2 −13n+3 4 n 2 −15n+9 2 n 2 −n−15 6 n 2 +13n−5 ⋅ 12 n 2 −13n+3 4 n 2 −15n+9

23.

36 x 2 −25 6 x 2 +65x+50 ⋅ 3 x 2 +32x+20 18 x 2 +27x+10 36 x 2 −25 6 x 2 +65x+50 ⋅ 3 x 2 +32x+20 18 x 2 +27x+10

For the following exercises, divide the rational expressions.

24.

3 y 2 −7y−6 2 y 2 −3y−9 ÷ y 2 +y−2 2 y 2 +y−3 3 y 2 −7y−6 2 y 2 −3y−9 ÷ y 2 +y−2 2 y 2 +y−3

25.

6 p 2 +p−12 8 p 2 +18p+9 ÷ 6 p 2 −11p+4 2 p 2 +11p−6 6 p 2 +p−12 8 p 2 +18p+9 ÷ 6 p 2 −11p+4 2 p 2 +11p−6

26.

q 2 −9 q 2 +6q+9 ÷ q 2 −2q−3 q 2 +2q−3 q 2 −9 q 2 +6q+9 ÷ q 2 −2q−3 q 2 +2q−3

27.

18 d 2 +77d−18 27 d 2 −15d+2 ÷ 3 d 2 +29d−44 9 d 2 −15d+4 18 d 2 +77d−18 27 d 2 −15d+2 ÷ 3 d 2 +29d−44 9 d 2 −15d+4

28.

16 x 2 +18x−55 32 x 2 −36x−11 ÷ 2 x 2 +17x+30 4 x 2 +25x+6 16 x 2 +18x−55 32 x 2 −36x−11 ÷ 2 x 2 +17x+30 4 x 2 +25x+6

29.

144 b 2 −25 72 b 2 −6b−10 ÷ 18 b 2 −21b+5 36 b 2 −18b−10 144 b 2 −25 72 b 2 −6b−10 ÷ 18 b 2 −21b+5 36 b 2 −18b−10

30.

16 a 2 −24a+9 4 a 2 +17a−15 ÷ 16 a 2 −9 4 a 2 +11a+6 16 a 2 −24a+9 4 a 2 +17a−15 ÷ 16 a 2 −9 4 a 2 +11a+6

31.

22 y 2 +59y+10 12 y 2 +28y−5 ÷ 11 y 2 +46y+8 24 y 2 −10y+1 22 y 2 +59y+10 12 y 2 +28y−5 ÷ 11 y 2 +46y+8 24 y 2 −10y+1

32.

9 x 2 +3x−20 3 x 2 −7x+4 ÷ 6 x 2 +4x−10 x 2 −2x+1 9 x 2 +3x−20 3 x 2 −7x+4 ÷ 6 x 2 +4x−10 x 2 −2x+1

For the following exercises, add and subtract the rational expressions, and then simplify.

33.

4 x + 10 y 4 x + 10 y

34.

12 2q − 6 3p 12 2q − 6 3p

35.

4 a+1 + 5 a−3 4 a+1 + 5 a−3

36.

c+2 3 − c−4 4 c+2 3 − c−4 4

37.

y+3 y−2 + y−3 y+1 y+3 y−2 + y−3 y+1

38.

x−1 x+1 − 2x+3 2x+1 x−1 x+1 − 2x+3 2x+1

39.

3z z+1 + 2z+5 z−2 3z z+1 + 2z+5 z−2

40.

4p p+1 − p+1 4p 4p p+1 − p+1 4p

41.

x x+1 + y y+1 x x+1 + y y+1

For the following exercises, simplify the rational expression.

42.

6 y − 4 x y 6 y − 4 x y

43.

2 a + 7 b b 2 a + 7 b b

44.

x 4 − p 8 p x 4 − p 8 p

45.

3 a + b 6 2b 3a 3 a + b 6 2b 3a

46.

3 x+1 + 2 x−1 x−1 x+1 3 x+1 + 2 x−1 x−1 x+1

47.

a b − b a a+b ab a b − b a a+b ab

48.

2x 3 + 4x 7 x 2 2x 3 + 4x 7 x 2

49.

2c c+2 + c−1 c+1 2c+1 c+1 2c c+2 + c−1 c+1 2c+1 c+1

50.

x y − y x x y + y x x y − y x x y + y x

Real-World Applications

51.

Brenda is placing tile on her bathroom floor. The area of the floor is 15 x 2 −8x−7 15 x 2 −8x−7 ft2. The area of one tile is x 2 −2x+1 ft 2 . x 2 −2x+1 ft 2 . To find the number of tiles needed, simplify the rational expression: 15 x 2 −8x−7 x 2 −2x+1 . 15 x 2 −8x−7 x 2 −2x+1 .

1.6 Rational Expressions - College Algebra 2e | OpenStax (1)

52.

The area of Lijuan's yard is 25 x 2 −625 25 x 2 −625 ft2. A patch of sod has an area of x 2 −10x+25 x 2 −10x+25 ft2. Divide the two areas and simplify to find how many pieces of sod Lijuan needs to cover her yard.

53.

Elroi wants to mulch his garden. His garden is x 2 +18x+81 x 2 +18x+81 ft2. One bag of mulch covers x 2 −81 x 2 −81 ft2. Divide the expressions and simplify to find how many bags of mulch Elroi needs to mulch his garden.

Extensions

For the following exercises, perform the given operations and simplify.

54.

x 2 +x−6 x 2 −2x−3 ⋅ 2 x 2 −3x−9 x 2 −x−2 ÷ 10 x 2 +27x+18 x 2 +2x+1 x 2 +x−6 x 2 −2x−3 ⋅ 2 x 2 −3x−9 x 2 −x−2 ÷ 10 x 2 +27x+18 x 2 +2x+1

55.

3 y 2 −10y+3 3 y 2 +5y−2 ⋅ 2 y 2 −3y−20 2 y 2 −y−15 y−4 3 y 2 −10y+3 3 y 2 +5y−2 ⋅ 2 y 2 −3y−20 2 y 2 −y−15 y−4

56.

4a+1 2a−3 + 2a−3 2a+3 4 a 2 +9 a 4a+1 2a−3 + 2a−3 2a+3 4 a 2 +9 a

57.

x 2 +7x+12 x 2 +x−6 ÷ 3 x 2 +19x+28 8 x 2 −4x−24 ÷ 2 x 2 +x−3 3 x 2 +4x−7 x 2 +7x+12 x 2 +x−6 ÷ 3 x 2 +19x+28 8 x 2 −4x−24 ÷ 2 x 2 +x−3 3 x 2 +4x−7

1.6 Rational Expressions - College Algebra 2e | OpenStax (2024)

FAQs

How do you solve rational expressions in Algebra 2? ›

Solving Rational Equations
  1. Completely factor all denominators.
  2. Multiply both sides of the equation by the least common denominator (LCD).
  3. Solve the resulting equation.
  4. Eliminate any solutions that would make the LCD become zero. These solutions are called extraneous solutions.
  5. Check the remaining solutions.

Discover More Details ›
What is a rational equation in Algebra 2? ›

A rational equation is a mathematical sentence that establishes an equivalent relationship between two expressions where one or more of their terms are rational expressions. The rational equation definition states that a rational equation has two sides, and both sides have rational expression terms.

Learn More Now ›
How do you add and subtract rational expressions in Algebra 2? ›

To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator. When the denominators are not the same, we must manipulate them so that they become the same.

See More ›
What are 2 examples of rational algebraic expression? ›

RATIONAL ALGEBRAIC EXPRESSION: Just for your own benefit, we define a rational number as a number expressed in the form of p/q where it is not equal to zero. ... Examples of rational expression are 5/x − 2, 4/(x + 1), (x + 5)/5, (x2 + 5x + 4)/(x + 5), (x + 1)/(x + 2), (x2 + x + 1)/2x etc.

See More ›
How to solve rational equations step by step? ›

Steps to Solve Rational Equations
  1. Note any value of the variable that would make any denominator zero.
  2. Find the least common denominator of all denominators in the equation.
  3. Clear the fractions by multiplying both sides of the equation by the LCD.
  4. Solve the resulting equation.
  5. Check:
May 13, 2023

Show Me More ›
How do you solve operations on rational algebraic expressions? ›

To add and subtract two rational expressions:
  1. Find a common denominator for the two expressions. ...
  2. Rewrite the equivalent form of each rational expression using the common denominator.
  3. Add or subtract the numerators of the expressions while retaining the common denominator.
  4. Combine like terms and write the result.

View More ›
What is an example of adding and subtracting rational algebraic expressions? ›

Example 1: Add: 3 y + 7 y . Solution: Add the numerators 3 and 7, and write the result over the common denominator, y. Example 2: Subtract: x − 5 2 x − 1 − 1 2 x − 1 . Solution: Subtract the numerators x − 5 and 1, and write the result over the common denominator, 2 x − 1 .

Read The Full Story ›
What are the steps for simplifying rational algebraic expressions? ›

Step 1: Factor the numerator and the denominator. Step 2: List restricted values. Step 3: Cancel common factors. Step 4: Reduce to lowest terms and note any restricted values not implied by the expression.

Find Out More ›
How do you solve problems involving rational algebraic expressions? ›

Six-Step Method for Applications of Rational Expressions
  1. Read the problem carefully and determine what you are asked to find.
  2. Assign a variable to represent the unknown.
  3. Write out an equation that describes the given situation.
  4. Solve the equation.
  5. State the answer using a nice clear sentence.

Keep Reading ›
How do you solve radical expressions in Algebra 2? ›

To solve a radical equation:
  1. Isolate the radical expression involving the variable. ...
  2. Raise both sides of the equation to the index of the radical.
  3. If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

Learn More ›

How to solve problems involving rational algebraic expressions? ›

Six-Step Method for Applications of Rational Expressions
  1. Read the problem carefully and determine what you are asked to find.
  2. Assign a variable to represent the unknown.
  3. Write out an equation that describes the given situation.
  4. Solve the equation.
  5. State the answer using a nice clear sentence.

Discover More ›
What is a rational function in Algebra 2? ›

A rational function is a function that is a fraction and has the property that both its numerator and denominator are polynomials. In other words, R(x) is a rational function if R(x) = p(x) / q(x) where p(x) and q(x) are both polynomials.

Learn More Now ›
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Author: Terence Hammes MD

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Author information

Name: Terence Hammes MD

Birthday: 1992-04-11

Address: Suite 408 9446 Mercy Mews, West Roxie, CT 04904

Phone: +50312511349175

Job: Product Consulting Liaison

Hobby: Jogging, Motor sports, Nordic skating, Jigsaw puzzles, Bird watching, Nordic skating, Sculpting

Introduction: My name is Terence Hammes MD, I am a inexpensive, energetic, jolly, faithful, cheerful, proud, rich person who loves writing and wants to share my knowledge and understanding with you.