Algebraic Manipulation Worksheets With Answers - Craven Community College Page 12
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29Complex Fractions
When both the numerator and the denominator of a complex fraction contain a single fraction, rewrite the
complex fraction as a division problem and do the indicated division. If the numerator or the denominator
contain more than one term, the terms must be combined before doing the division.
Example:
2X + 8
4
X – X
3
Working the numerator first
2X + 8 = 2X + 8 • 4
Rewrite using the LCD
4
4
1 4
=
2X + 32
Add
4
=
2(X + 16)
Simplify
4
=
X + 16
2
Working the denominator next
X – X = X – X • 3
Rewrite using the LCD
3
3
1 3
=
X – 3X
Subtract
3
=
-2X
Simplify
3
Thus
2X + 8
X + 16
4
=
2
X – X
-2X
3
3
X + 16
÷
-2X
Write as a division problem
2
3
X + 16
•
3
Write as equivalent multiplication problem
2
-2X
-3(X + 16)
4X
Multiply and Simplify
12
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