1. 9.3 Simplifying and Multiplying Rational Expressions 4/26/2013

2. Example 1 Simplify a Rational Expression Simplify the rational expression, if possible. a. 5 15x c. 14x 2 6x6x = 3 5 x 5 3x3x = Divide out the common factor 5 and simplify. b. x x 5 + This expression is already in simplest form. 2 7 x x = 2 3 x = 7x7x 3 Divide out the common factors 2 and x.

3. Checkpoint Simplify a Rational Expression 9x9x ( 121 x ( + 3. x x1– 4. ANSWER 3x3x ( 41 x ( + already in simplest form 1. Simplify the expression, if possible. 4x4x 10 ANSWER 2x2x 5 2 x 2. 8 4x4x

4. Checkpoint Simplify the expression, if possible. Write in Simplest Form 5. 2x2x 12x2x + ANSWER already in simplest form 6. 3x3x () 1x +3x 23x 2 ANSWER x () 1x +

5. Checkpoint Write in Simplest Form Simplify the expression, if possible. 7. 12x 8x8x2x 22x 2 + ANSWER 6 4x + 8. 2 x+ 6 3x3x + ANSWER 3 1

6. Example 3 Multiply Rational Expressions Multiply. Simplify the result. 3x3x 4x 24x 2 9x9x 8x 58x 5 SOLUTION 3x3x 4x 24x 2 9x9x 8x 58x 5 = 2x 32x 3 3 1 2 1 3 Subtract exponents of x

7. Example 4 Multiply Rational Expressions Multiply. Simplify the result. x x 2x 2 9 – 4x4x 3x3x 12 – SOLUTION x x 2x 2 9 – 4x4x 3x3x 12 – = 4 () 3x +3 Factor the numerators and denominators. = 4 3x3x () 3x – x () 3x – () 3x +

8. Checkpoint Multiply the rational expressions. Simplify the result. Multiply Rational Expressions 9. 14 3x3x7x7x 6x 36x 3 ANSWER 4x4x 1 x 2x 2 2x2x4 – 3x3x 2x2x 6 – 10. ANSWER 3x3x 4 x 2x 2 6x6x 4 – 11. 4x4x8 + x 3x 3 ANSWER 24 x 2x 2 () 2x –

9. Example 5 Multiply by a Polynomial Multiply. Simplify the result. ( 2 – ( 3 x x 2x 2 – 65x5x + x Factor out of. 1 – ( 2 x – ( = x ( x – ( ( x – ( 231 1 – ( x – ( 32 SOLUTION x x 2x 2 + 5x5x6 ( 2 – ( 3 x – Write polynomial as a rational expression. = 1 x x 2x 2 + 5x5x6 ( 2 – ( 3 x – Simplify. = x – 3x3x – 3

10. Checkpoint Multiply by a Polynomial ANSWER 8 x 2x 2 3 Multiply the expressions. Simplify the result. x + 4 12. 2x2x ( ( + 3 6 x 13. 3x3x + x 2x 2 ( ( + 12 4x4x 3x3x 14. x 2x 2 –– ( 2 – ( x2 x ANSWER x 3x3x – + 1

11. Homework: 9.3 p.483 #22-52 even only I’m reading a book about anti-gravity. I can’t put it down!!!