1. Joyce DuVall Green Valley High School Henderson, Nevada

2. Multiplying Rational Expressions  The objective is to be able to multiply rational expressions.

3. Step 1  Multiply the numerators. Multiply the following rational expressions. 36 316 2 5 x x 

4. Step 2 Multiply the denominators 36 316 2 5 x x 

5. Step 3 Simplify the resulting expression by dividing out the greatest common factor of the numerator and denominator. The greatest common factor (GCF) of 36 and 48 is 12. The greatest common factor (GCF) of x 2 and x 5 is x 2.

6. Simplify 312 4 2 23   x xx 3 4 2 23  x xx 11 3 4 3 4 33  xx

7. Method 2 When the rational expressions become more complex or the numbers become larger, it is sometimes easier to divide out the common factors and then multiply. This is the case for the following example.

8. Example Factor each term. Divide out the common factors

9. 11   4 xy 4  xy Example Continued Simplify

10. AA A

11. 27 3 34 57 2 2     aa a Factor each expression Divide out common factors 3 3 7 7 24 5 2 2   a a a Simplify and multiply 111 8 5 8 5  aa You Try It

12. Factor each expression  5 9 2 3  rs v 45 39 23 22   vv rrss Divide out common factors 5 5 9 9  r r 2 2 s s 3 2 2 4   v rs Simplify and multiply 11111  3 2 2 4v rs 2 4 3 2 v 3 3 v v You Try It

13. Factor each expression ) 4x 421(x    )34()(xx  21x  Divide out common factors  Simplify and multiply 11   )43 1  (x3  4()x  1 12 2 x x   4 4 x x   43 1 x() You Try It