Joyce DuVall Green Valley High School Henderson, Nevada

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

Step 1  Multiply the numerators. Multiply the following rational expressions x x 

Step 2 Multiply the denominators x x 

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.

Simplify   x xx  x xx  xx

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.

Example Factor each term. Divide out the common factors

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

AA A

    aa a Factor each expression Divide out common factors   a a a Simplify and multiply  aa You Try It

Factor each expression   rs v   vv rrss Divide out common factors  r r 2 2 s s   v rs Simplify and multiply  v rs v 3 3 v v You Try It

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