Multiply the numerator and the denominator of each expression by any factor(s) needed to convert the denominator into the LCD. 3. Add or subtract nume...

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Name ________________ Adding and Subtracting Rational Expressions Module 1, Unit 2, Lesson 16

Adding and Subtracting Rational Expressions When adding or subtracting rational expressions with no common denominator : 1. Find the Least Common Denominator (LCD) a. Factor each denominator completely. b. List the factors of the first denominator. c. Add to the list in step (b) any factors of the second denominator that do not already appear. d. Form the product of the factors. This product is the LCD. 2. Rewrite each rational expression as an equivalent expression whose denominator is the LCD. a. Multiply the numerator and the denominator of each expression by any factor(s) needed to convert the denominator into the LCD. 3. Add or subtract numerators and place the resulting expression over the LCD. 4. Simplify, if possible.

3 5x 5 x 2 25 x 2 4

3 5x (5 x 2) (5 x 2)(5 x 2) 3(5 x 2) 5x (5 x 2)(5 x 2) (5 x 2)(5 x 2) 15 x 6 5 x (5 x 2)(5 x 2) 20 x 6 (5 x 2)(5 x 2)

Write each sum or difference as a single rational expression. 5 2 3 7 3 1. 2. 6 8 4 10

1 1 x 5 x 5

3.

x 3 x 2x 2y 4 y 3 y

4.

5.

1 a a2 2a

6. 1

7.

4 m 3 m 2m 6

8.

9.

3x x4 x 3 x 2

10.

1 2 x

4 5 x 6x 9 x 3 2

x x 2 x 2 x 24 x 7 x 6 2