MTH 100
Adding and Subtracting Rational
Expressions
Objectives
1. Add or subtract rational expressions that
have a common denominator.
2. Add or subtract rational expressions that do
not have a common denominator.
Objective 1: Common Denominators
1. Combine the terms in the numerator as best
you can. Write the result over the common
denominator.
2. Check to see if the rational expression can be
reduced to lowest terms (factor and cancel).
Examples
9w
5w

3
3
4ab 4ab
x3
x7

2
2
x  8 x  15 x  8 x  15
Objective 2: Uncommon Denominators
1. Find a common denominator: every factor
represented, no factor needlessly repeated.
2. Write each rational expression with the common
denominator (change the bottom, change the
top).
3. Combine the terms in the numerator as best you
can. Write the result over the common
denominator.
4. Check to see if the rational expression can be
reduced to lowest terms (factor and cancel).
Examples
4
9

4 5
3 6
5a b 10a b
7 y 1
1 6 y

2
2
y  25 y  10 y  25
More Examples
6
x 8
3x


2
x  4 2 x 10  5 x
x 5 x 5

x 5 x 5
Still More Examples
x 5
x 5

2
x  8 x  15 x  3
4 x 3x  7

x6 6 x
2