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w 2 3 w 28 49 w 2

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Multiply and Divide Rational Expressions

Multiply Rational Expressions

In the following exercises, multiply.

2 x y 2 8 y 3 · 16 y 24 x

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3 a 2 + 21 a a 2 + 6 a 7 · a 1 a b

3 b

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5 z 2 5 z 2 + 40 z + 35 · z 2 1 3 z

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Divide Rational Expressions

In the following exercises, divide.

t 2 4 t + 12 t 2 + 8 t + 12 ÷ t 2 36 6 t

6 t ( t + 6 ) ( t + 6 )

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r 2 16 4 ÷ r 3 64 2 r 2 8 r + 32

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11 + w w 9 ÷ 121 w 2 9 w

1 11 + w

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3 y 2 12 y 63 4 y + 3 ÷ ( 6 y 2 42 y )

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c 2 64 3 c 2 + 26 c + 16 c 2 4 c 32 15 c + 10

5 c + 4

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8 m 2 8 m m 4 · m 2 + 2 m 24 m 2 + 7 m + 10 ÷ 2 m 2 6 m m + 5

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Add and Subtract Rational Expressions with a Common Denominator

Add Rational Expressions with a Common Denominator

In the following exercises, add.

4 a 2 2 a 1 1 2 a 1

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p 2 + 10 p p + 5 + 25 p + 5

p + 5

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Subtract Rational Expressions with a Common Denominator

In the following exercises, subtract.

d 2 d + 4 3 d + 28 d + 4

d + 7

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z 2 z + 10 100 z + 10

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4 q 2 q + 3 q 2 + 6 q + 5 3 q 2 q 6 q 2 + 6 q + 5

q 3 q + 5

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5 t + 4 t + 3 t 2 25 4 t 2 8 t 32 t 2 25

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Add and Subtract Rational Expressions whose Denominators are Opposites

In the following exercises, add and subtract.

18 w 6 w 1 + 3 w 2 1 6 w

15 w + 2 6 w 1

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a 2 + 3 a a 2 4 3 a 8 4 a 2

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2 b 2 + 3 b 15 b 2 49 b 2 + 16 b 1 49 b 2

3 b 2 b + 7

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8 y 2 10 y + 7 2 y 5 + 2 y 2 + 7 y + 2 5 2 y

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Add and Subtract Rational Expressions With Unlike Denominators

Find the Least Common Denominator of Rational Expressions

In the following exercises, find the LCD.

4 m 2 3 m 10 , 2 m m 2 m 20

( m + 2 ) ( m 5 ) ( m + 4 )

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6 n 2 4 , 2 n n 2 4 n + 4

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5 3 p 2 + 17 p 6 , 2 m 3 p 2 23 p 8

( 3 p + 1 ) ( p + 6 ) ( p + 8 )

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Find Equivalent Rational Expressions

In the following exercises, rewrite as equivalent rational expressions with the given denominator.

Rewrite as equivalent rational expressions with denominator ( m + 2 ) ( m 5 ) ( m + 4 ) :

4 m 2 3 m 10 , 2 m m 2 m 20 .
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Rewrite as equivalent rational expressions with denominator ( n 2 ) ( n 2 ) ( n + 2 ) :

6 n 2 4 n + 4 , 2 n n 2 4 .

6 n + 12 ( n 2 ) ( n 2 ) ( n + 2 ) ,
2 n 2 4 n ( n 2 ) ( n 2 ) ( n + 2 )

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Rewrite as equivalent rational expressions with denominator ( 3 p + 1 ) ( p + 6 ) ( p + 8 ) :

5 3 p 2 + 19 p + 6 , 7 p 3 p 2 + 25 p + 8
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Add Rational Expressions with Different Denominators

In the following exercises, add.

2 c 2 + 9 c + 3

11 c 12 ( c 2 ) ( c + 3 )

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3 d d 2 9 + 5 d 2 + 6 d + 9

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2 x x 2 + 10 x + 24 + 3 x x 2 + 8 x + 16

5 x 2 + 26 x ( x + 4 ) ( x + 4 ) ( x + 6 )

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5 q p 2 q p 2 + 4 q q 2 1

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Subtract Rational Expressions with Different Denominators

In the following exercises, subtract and add.

3 v v + 2 v + 2 v + 8

2 ( v 2 + 10 v 2 ) ( v + 2 ) ( v + 8 )

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−3 w 15 w 2 + w 20 w + 2 4 w

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7 m + 3 m + 2 5

2 m 7 m + 2

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n n + 3 + 2 n 3 n 9 n 2 9

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8 d d 2 64 4 d + 8

4 d 8

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Simplify Complex Rational Expressions

Simplify a Complex Rational Expression by Writing it as Division

In the following exercises, simplify.

5 a a + 2 10 a 2 a 2 4

a 2 2 a

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x 3 x x + 5 1 x + 5 + 1 x 5

( x 8 ) ( x 5 ) 2

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Simplify a Complex Rational Expression by Using the LCD

In the following exercises, simplify.

6 + 2 q 4 5 q + 4

( q 2 ) ( q + 4 ) 5 ( q 4 )

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3 a 2 1 b 1 a + 1 b 2

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2 z 2 49 + 1 z + 7 9 z + 7 + 12 z 7

z 5 23 z + 21

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3 y 2 4 y 32 2 y 8 + 1 y + 4

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Solve Rational Equations

Solve Rational Equations

In the following exercises, solve.

1 b 2 + 1 b + 2 = 3 b 2 4

3 2

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3 q + 8 2 q 2 = 1

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v 15 v 2 9 v + 18 = 4 v 3 + 2 v 6

no solution

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Solve a Rational Equation for a Specific Variable

In the following exercises, solve for the indicated variable.

V l = h w for l

l = V h w

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x = y + 5 z 7 for z

z = y + 5 + 7 x x

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Solve Proportion and Similar Figure Applications Similarity

Solve Proportions

In the following exercises, solve.

In the following exercises, solve using proportions.

Questions & Answers

what is mutation
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what is a cell
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how is urine form
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classification of plants, gymnosperm features.
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What is Atoms
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urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
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how is urine formed in human
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malaria is caused by an insect called mosquito.
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Malaria is cause by female anopheles mosquito
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Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
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a canal is more needed in a root but a cavity is a bad effect
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what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
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how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
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stimulates the follicle to release the mature ovum into the oviduct
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what are the functions of Endocrine and pituitary gland
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endocrine secrete hormone and regulate body process
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while pituitary gland is an example of endocrine system and it's found in the Brain
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what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
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biology is the study of life.
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Biology is the study of how living organisms live and survive in a specific environment
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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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