1. 3.10 Warm Up Do # 4, 8, & 12 on pg. 268 Do # 4, 8, & 12 on pg. 268

2. 3.10 Add & Subtract Rational Expressions

3. To +/- Rational expressions must have common denominators Rational expressions must have common denominators Least Common Denominator (LCD): factor each denominator and multiply by each factor only once Least Common Denominator (LCD): factor each denominator and multiply by each factor only once Multiply each numerator by the LCD Multiply each numerator by the LCD Simplify the numerator & write it over the denominator (LCD) Simplify the numerator & write it over the denominator (LCD) Simplify Simplify

4. Key to Subtracting!!! CHANGE THE SIGN OF EVERY TERM THAT IS SUBTRACTED!!! CHANGE THE SIGN OF EVERY TERM THAT IS SUBTRACTED!!!

5. EXAMPLE 1 Add and subtract with the same denominator a. 5 3x3x 7 3x3x += 12 3x3x Add numerators. Factor and divide out common factor. 3 4 3 x = = 4 x Simplify. b. 3x3x x – 1 – = x + 5 x – 1 3x – (x + 5) x – 1 Subtract numerators. 2x – 5 x – 1 = Simplify.

6. GUIDED PRACTICE for Example 1 Find the sum or difference. 1. 2 y + y + 1 y = y + 3 y 2x + 4 2x – 1 =2. 4x + 1 2x – 1 2x – 3 2x – 1 –

7. EXAMPLE 3 Add expressions with different denominators Find the sum 5 12x 3 9 8x28x2 +

8. EXAMPLE 4 Subtract expressions with different denominators Find the difference –. 7x7x x + 2 10 3x3x

9. EXAMPLE 5 Subtract expressions with different denominators Find the difference. x + 4 x 2 + 3x – 10 – x – 1 x 2 + 2x – 8 x + 4 x 2 + 3x – 10 – x – 1 x 2 + 2x – 8 Factor denominators. Rewrite fractions using LCD, (x – 2)(x + 5)(x + 4). Subtract fractions. = x + 4 (x – 2)(x + 5) – x – 1 (x + 4)(x – 2) = (x + 4)(x + 4) (x – 2)(x + 5) (x + 4) – (x – 1)(x + 5) (x + 4)(x – 2)(x + 5) = (x + 4)(x + 4) – (x – 1)(x + 5) (x – 2)(x + 5)(x + 4)

10. EXAMPLE 5 Subtract expressions with different denominators = x 2 + 8x + 16 – (x 2 + 4x – 5) (x – 2)(x + 5)(x + 4) = 4x + 21 (x – 2)(x + 5)(x + 4) Find products in numerator. Simplify.

11. GUIDED PRACTICE for Examples 3, 4, and 5 Find the sum or difference. 6. 3 2x2x 7 5x 4 + = 15x 3 + 14 10x 4 7. y y + 1 + 3 y + 2 = y 2 + 5y + 3 ( y +1)( y + 2) 8. 2z – 1 z 2 + 2z – 8 – z + 1 z 2 – 4 = z 2 – 2z – 6 (z + 4)(z – 2)(z + 2)