1. Welcome to Algebra 2 Rational Equations: What do fractions have to do with it?

2. Agenda  Review Test 2-4 Corrections due 4/28/16  8-1: Operations with rational expressions  8-6: Solving rational equations  HW: p. 533 #1-12, all and p. 576 #1-7, odd

3. Definition  A rational expression is the ratio of two polynomial expressions.

4. SIMPLIFYING RATIONAL EXPRESSIONS Step 1: Factor numerator and denominator “when in doubt, write it out!!” Step 2: Cancel common factors Step 3: Simplified form

5. Simplify Assume the denominator cannot equal zero.

6. Example 1 Simplify a rational expression x² + 7x + 10 x² - 4 Step 1: Factor numerator and denominator (x² + 7x + 10) = (x+2)(x+5) (x² - 4) (x+2)(x-2) Step 2: Cancel common factors (x+2)(x+5) (x+2)(x-2) Step 3: Simplified Form x + 5 x - 2

7. Your Turn Simplify the expression 1. x² - 2x – 15 x² + 4x + 3 (x – 5)(x + 3) (x + 1)(x + 3) x – 5 x + 1

8. Multiplying rational expressions Factor and reduce before multiplying.

9. Multiply rational expressions Factor, Multiply and Cancel

10. Your Turn Multiply the expression 6x² + 18x x² - x – 2 x² + x – 6 * x² - 7x – 8 6x(x + 3)(x-2)(x+1) (x+3)(x-2)(x-8)(x+1) 6x x-8

11. More Examples  Multiply the expressions. Simplify the result.

12. Divide the Rational Expressions Multiply by the reciprocal:

13. Your Turn Divide rational expressions Step 1: Multiply by reciprocal 3 x² + 6x – 7 x+7 * 8x² - 8x Step 2: Factor and Multiply 3 (x+7)(x-1) (x+7)(8x)(x-1)

14. More Examples  Divide each expression. Simplify the result.

15. Checkpoint Divide the expression 3. (x – 5) (2x² - 5x + 2) (9x² - 18x)(2x² - 11x + 5) (x – 5)(2x-1)(x-2) 9x(x–2)(2x-1)(x-5) 1_ 9x