Section 6.2 Multiplying & Dividing Rational Expressions  Multiplying Rational Expressions  Finding Powers of Rational Expressions  Dividing Rational Expressions  Mixed Operations

Multiplying Fractions (Parenthesize polynomials for clarity) To Simplify: Factor, then cancel like factors

Example – Step by Step x 1. Write down original problem 2. Combine with parenthesized polynomials 3. Factor polynomials (if possible) 4. Rewrite (if any factoring was done) 5. Cancel out matching factors 6. Simplify the answer

Practice - Rational Multiplication 1. Write down original problem 2. Combine with parenthesized polynomials 3. Factor polynomials (if possible) 4. Rewrite (if any factoring was done) 5. Cancel out matching factors 6. Simplify the answer

Practice - Rational Multiplication 1. Write down original problem 2. Combine with parenthesized polynomials 3. Factor polynomials (if possible) 4. Rewrite (if any factoring was done) 5. Cancel out matching factors 6. Simplify the answer

Practice - Rational Multiplication 1. Write down original problem 2. Combine with parenthesized polynomials 3. Factor polynomials (if possible) 4. Rewrite (if any factoring was done) 5. Cancel out matching factors 6. Simplify the answer

Finding Powers of Rational Expressions  Factor and Simplify (if possible) before applying the power  If part of a larger expression, see if any terms cancel out  Usually leave in factored form (unlike the text example)

Dividing Fractions Change to multiplication by reciprocal, then follow the procedure for multiplication

Practice - Rational Division 1. Write down original problem 1a. Rewrite as multiplication by reciprocal 2. Combine with parenthesized polynomials 3. Factor polynomials (if possible) 4. Rewrite (if any factoring was done) 5. Cancel out matching factors 6. Simplify the answer

Practice - Rational Division 1. Write down original problem 1a. Rewrite as multiplication by reciprocal 2. Combine with parenthesized polynomials 3. Factor polynomials (if possible) 4. Rewrite (if any factoring was done) 5. Cancel out matching factors 6. Simplify the answer

Practice - Rational Division 1. Write down original problem 1a. Rewrite as multiplication by reciprocal 2. Combine with parenthesized polynomials 3. Factor polynomials (if possible) 4. Rewrite (if any factoring was done) 5. Cancel out matching factors 6. Simplify the answer

Mixed Operations  Multiplications & Division are done left to right  In effect, make each divisor into a reciprocal

Homework Multipying & Dividing Rational Expressions Wrksht What Next? Adding & Subtracting Rational Expressions