Operations on Rational Operations on Rational Expressions ReviewExpressions Review

Test Tomorrow!!!Test Tomorrow!!!

A _____________ expression is A _____________ expression is an expression that can be an expression that can be written as a ratio of two written as a ratio of two

polynomialspolynomials..A. RadicalA. Radical

C.C.BinomialBinomial

B. B. RelationalRelational

D. D. RationalRational

Simplifying a Rational Simplifying a Rational ExpressionExpression

Finding the excluded values. (What Finding the excluded values. (What values of x make the rational expression values of x make the rational expression undefined?)undefined?) A rational expression is undefined when the A rational expression is undefined when the

value of x causes the denominator to equal value of x causes the denominator to equal zero.zero.

3 9

x

x

Set the denominator equal to zero and solve for x

3 9 0

3 9

3

x

x

x

The expression is undefined when x = 3

Find the excluded value of the Find the excluded value of the expression:expression:

A. (x-3)A. (x-3)(x+5)(x+5)

C. (x+5)(x-C. (x+5)(x-3) 3)

B. X = 3, -5B. X = 3, -5

D. X = -3, 5D. X = -3, 5

2

2

2 15

x

x x

Simplify the expression by Simplify the expression by dividing out the common dividing out the common

monomialsmonomials

Factor numerator and denominator Factor numerator and denominator completely, then divide out common completely, then divide out common factors.factors.

2

3

7 14

14

q q

q

7 ( 2)

14

q q

q q q

7 ( 2)

7

q q

q q q

Simplify the expression:Simplify the expression:

A.A.

C.C.

B.B.

D.D.

3

5

3

15

x

x

25

x

x

2

5

x

2

1

5x1

5x

Simplify the expression:Simplify the expression:

A.A.

C.C.

B.B.

D.D.

28

7 21

x

x 4

3

x

x 3

x

x

28

7 21x 4

21

x

x

Multiply rational expressions Multiply rational expressions involving polynomials:involving polynomials:

Multiply numerators and denominatorsMultiply numerators and denominators Factor if possibleFactor if possible Divide out common factorsDivide out common factors

2

5

4 5

15 8

x

x

214 x

315

15

2 8

5x 3x 3

1

6x

Find the product:Find the product:

A.A.

C.C.

B.B.

D. D.

6

2

24 14

7 40

x

x

6

2

336

280

x

x

4336

280

x

321

5

x 46

5

x

Find the Quotient:Find the Quotient:

Change the division Change the division to multiplicationto multiplication

Flip the second Flip the second fractionfraction

Cross simplify if Cross simplify if possiblepossible

Multiply numerators Multiply numerators and denominatorsand denominators

3 2

24 6

5 25x x

2

3

24 25

5 6

x

x

4 24

15 3x

5 25

x

2x

16

20

x

Find the quotient:Find the quotient:

A.A.

C.C.

B.B.

D. D.

4

2

11 22

18 9

x

x

2242

162

x

2121

81

x 6

4

x

2x

How can you find the least How can you find the least common multiple of common multiple of

polynomials?polynomials? Step One: Write Step One: Write

the factors of each the factors of each expressionexpression

Step Two: Find Step Two: Find Common FactorsCommon Factors

Step Three: Step Three: MultiplyMultiply

2

6 2 3

8 2 2 2

x x

x x x

2

6 2 3

8 2 2 2

x x

x x x

LCM 2 3 2 2x x

Use common factors only once.

Find the LCM of 9x and Find the LCM of 9x and 4x4x

A.A.

C.C.

B.B.

D.D.

3

336x 36x

18x 324x

Add and subtract – Same Add and subtract – Same denominatordenominator

Add numeratorsAdd numerators

Factor and Factor and divide out divide out common factorscommon factors

SimplifySimplify

2 8

5 5x x

10

5x

210

5 x

2

x

Find the sum or difference:Find the sum or difference:

A.A.

C.C.

B.B.

D.D.

3 2

7 7

x x

x x

2 1

7

x

x

2 1

7

x

x

2 1

14

x

x

2

2 1

14

x

x

Find the sum or difference:Find the sum or difference:

A.A.

C.C.

B.B.

D.D.

5 7 2 9

3 4 3 4

x x

x x

3 16

3 4

x

x

3 16

3 4

x

x

8 2

3 4

x

x

8 2

3 4

x

x

Add expressions with different Add expressions with different denominatorsdenominators

Rewrite fraction Rewrite fraction using LCDusing LCD

Simplify Simplify numerators and numerators and denominatorsdenominators

Add fractionsAdd fractions

11 4

2 7x x

77 8

14 14x x

1177

714

2 4

x

8

12 14 x

22

7x

Find the sum or difference:Find the sum or difference:

A.A.

C.C.

B.B.

D.D.

8 5

3 12x x

3

36x81

36x

27

12x

37

12x

Find the sum or difference:Find the sum or difference:

A.A.

C.C.

B.B.

D.D.

3

6 7

5 15x x

4

13

20x

2

3

18 7

15

x

x

2

3

11

15

x

x

5

3x