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

4

)3(

)3)(20(

)5)(3)(3(

)3)(20(

)5)(96(

3

5

20

96 22222

xx

xx

xxx

xx

xxx

x

x

x

xx1

4 1 1

1 x

1. Write down original problem2. Combine with parenthesized polynomials 3. Factor polynomials (if possible)4. Rewrite (if any factoring was done)5. Cancel out matching factors6. Simplify the answer

Practice - Rational Multiplication

1. Write down original problem2. Combine with parenthesized polynomials 3. Factor polynomials (if possible)4. Rewrite (if any factoring was done)5. Cancel out matching factors6. Simplify the answer

Practice - Rational Multiplication

1. Write down original problem2. Combine with parenthesized polynomials 3. Factor polynomials (if possible)4. Rewrite (if any factoring was done)5. Cancel out matching factors6. Simplify the answer

Practice - Rational Multiplication

1. Write down original problem2. Combine with parenthesized polynomials 3. Factor polynomials (if possible)4. Rewrite (if any factoring was done)5. Cancel out matching factors6. 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 problem1a. 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 factors6. Simplify the answer

Practice - Rational Division

1. Write down original problem1a. 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 factors6. Simplify the answer

Practice - Rational Division

1. Write down original problem1a. 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 factors6. Simplify the answer

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

HomeworkMultipying & Dividing Rational Expressions Wrksht

What Next?Adding & Subtracting Rational Expressions