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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