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
โ
โ
โ
+
1
5
1
21
w
ww
find the LCD of the three inner fractions. LCD is
)1(
โ
ww
o
โ
โ
โ
โ
โ
+
โ
1
)1(5
1
)1(2)1(1
w
ww
w
ww
w
ww
clear fractions by distributing the LCD to all the numerators
o โ
โ
โ
โ
โ
+
โ
)1(
)1(5
)1(
)1(2)1(1
w
ww
w
ww
w
ww
reduce all three fractions within the complex fraction
o
โ
โ
โ
+
โ
w
w
w
ww
5
13
5
21
combine like terms and reduce if possible.
๎ Evaluate the rational expression given a numerical value for each variable.
Example: Given
23
โ
=
=
yx
o
โ
โ
โ
32
4
14
)5(
xy
x
change all variables to empty parentheses then substitute the number
o
โ
โ
โ
32
4
)(14)(
)5)((
use the parentheses to avoid errors when substituting
o
โ
โโ
โ
32
4
)3(14)2(
)5)3((
use order of operations to evaluate to a single number
o
โโโ
โ
187
8
374
16
reduce if possible
