And Evaluating Rational Expressions - Mt. San Antonio College

Math 51

Worksheet

Complex Fractions

And

Evaluating Rational Expressions

A rational expression with fractions in the numerator, denominator or both is called a complex

fraction. Simplify by clearing fractions using the LCD of all the fractions within the expression.

o

1

2

+

w w ?1

5

w ?1

? find the LCD of the three inner fractions. LCD is w ( w ? 1)

o

1w ( w ? 1) 2 w ( w ? 1)

+

w

w ?1

5w ( w ? 1)

w ?1

? clear fractions by distributing the LCD to all the numerators

o

1w ( w ? 1) 2 w ( w ? 1)

+

w

( w ? 1)

5w ( w ? 1)

( w ? 1)

? reduce all three fractions within the complex fraction

o

w ? 1 + 2w

?

5w

3w ? 1

? combine like terms and reduce if possible.

5w


Evaluate the rational expression given a numerical value for each variable.

Example: Given x = 3

y = ?2

4

o

( x ? 5)

y 2 ? 14 x 3

o

(( ) ? 5) 4

( ) 2 ? 14( ) 3

o

((3) ? 5) 4

(?2) 2 ? 14(3) 3

o

16

8

? ?

? 374

187

? change all variables to empty parentheses then substitute the number

? use the parentheses to avoid errors when substituting

?

use order of operations to evaluate to a single number

? reduce if possible

Practice Problems

Evaluate each rational expression when x = ?3

y = 4 z = ?1

1)

( x ? z ) 36

y2

2)

? x + x 2 ? 4 yz

2y

3)

2 y 3 ? 6x 2 ? 8z

8x + 6

4)

( ?4 z + y ) 3

5x 2

Simplify each complex fraction

5)

1 2

+

a b

a +1

ab

7)

1

2

?

m +1 m ?1

2

1

+

m ?1 m +1

4

2

6)

8)

?

3

xy 2

x y

1

+3

xy

3

x ? 16

1

x+4

2

Answer Key

1)

3)

5)

7)

3

4

41

?

9

2a + b

a +1

?

?

m+3

3m + 1

2)

4)

6)

8)

1

512

45

4 y ? 3x

xy + 3 x 2 y 2

3

x?4

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