Name Date
WORKSHEET 6.9: ADDING AND SUBTRACTING ALGEBRAIC
FRACTIONS WITH UNLIKE DENOMINATORS
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Follow the steps below to add or subtract algebraic fractions with unlike denominators.
Assume that the denominators of the fractions are not equal to zero.
- Find the least common denominator (select the largest exponent of every factor).
- Write equivalent fractions.
- Add or subtract.
- Simplify, if possible.
EXAMPLE
2
x+ 3
−
1
x+ 1
The least common denominator is (x+ 3 )(x+ 1 ) because the factors are (x+ 3 )and(x+ 1 ).
The largest exponent of each factor is 1.
Write equivalent fractions and subtract.
2
x+ 3
·
x+ 1
x+ 1
−
1
x+ 1
·
x+ 3
x+ 3
=
2 x+ 2 −x− 3
(x+1)(x+3)
=
x− 1
(x+1)(x+3)
This fraction cannot be simplified.
DIRECTIONS: Find each sum or difference.
1.
x
4
+
2 x
9
1
x+ 1
−
1
x
2
x
+
3
x^2
6
x+ 3
−
2
x− 3
5.
3 x− 2
6
−
x− 3
9
CHALLENGE:Shawn found the sum of
3
x+ 1
and
5
(x+1)^2
. He added the
numerators and found the sum to be
8
(x+1)^2
. Do you agree with his
answer? Explain your reasoning.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.