1. AIM: How do we simplify complex fractions? Do Now: Perform the operation: 1) x__ + 1__ x + 2 x – 2 2) 2z - z²_ z - 1 z² - 1 HW # 9 – pg 64 #11,12,13 (Review Sheet) Test on Thursday – Collect HW folders

2. Complex Fractions A complex fraction is an expression having a fraction in the numerator, denominator, or both. Examples of complex fractions include a 2 – 16 a + 2. a – 3 a 2 + 4

3. Preferred method: since the fraction bar means division, change the expression to a division problem and divide.

4. Complex Fractions Simplifying a Complex Fraction: Preferred Method Step 1 Simplify the numerator and denominator separately. Step 2 Divide by multiplying the numerator by the reciprocal of the denominator. Step 3 Simplify the resulting fraction, if possible.

5. Complex Fractions EXAMPLE 1 Simplifying Complex Fractions by PM Use Method 1 to simplify each complex fraction. (a) d + 5 3d3d d – 1 6d6d = d + 5 3d3d d – 1 6d6d ÷= d + 5 3d3d 6d6d d – 1 · = 2( d + 5) ( d – 1) Write as a division problem. Multiply by the reciprocal of. d – 1 6d6d Simplify. Both the numerator and the denominator are already simplified, so divide by multiplying the numerator by the reciprocal of the denominator. 2

6. Complex Fractions EXAMPLE 1 Simplifying Complex Fractions by PM Use PM to simplify each complex fraction. Simplify the numerator and denominator. (Step 1) Write as a division problem. 3 x + 1 x Multiply by the reciprocal of. (Step 2) (b) 2 x 5 – 3 x 1 + = x 5 – x 2x2x x 1 + x 3x3x = x 2 x – 5 x 3 x + 1 ÷ = x 2 x – 5 x 3 x + 1 · = x 2 x – 5 3 x + 1 x = 2 x – 5 Multiply and simplify. (Step 3)

7. Try an Example: simplify the expression 2

8. If time: a + b a – b_____ a - b