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

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3.10 Add & Subtract Rational Expressions

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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

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

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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.

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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 –

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

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

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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)

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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.

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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)

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