11 4 Adding and Subtracting Rational Expressions Hubarth

11 -4 Adding and Subtracting Rational Expressions Hubarth Algebra

Ex 1 Adding Expressions With Like denominators 4 2 Add x + 3 and x + 3. 4 x+3 + 2 x+3 = 4+2 x+3 Add the numerators only. = 6 x+3 Simplify the numerator.

Subtracting Expressions With Like Denominators Subtract 3 x + 5 + 2 x – 8 3 x 2 4 x + 7 2 3 x + 2 x – 8 – from 3 x + 5 2 3 x + 2 x – 8 4 x + 7 + 2 x – 8 3 x 2 = 4 x + 7 – (3 x + 5) 3 x 2 + 2 x – 8 Use the Distributive Property. = x+2 + 2 x – 8 = 3 x 2 = 1 x+2 (3 x – 4) (x + 2) Simplify the numerator. 1 = Subtract the numerators. 1 3 x – 4 Factor the denominator. Divide out the common factor x + 2. Simplify.

Ex 3 Adding Expressions With Monomial Denominators 1 3 Add 4 x + 8 4 x = 2 • x Factor each denominator. 8=2 • 2 LCD = 2 • 2 • x = 8 x Step 2: Rewrite using the LCD and add. 3 1 + = 4 x 8 2 • 3 1 • x + 2 • 4 x 8 • x 6 x Rewrite each fraction using the LCD. = 8 x + 8 x Simplify numerators and denominators. = Add the numerators.

Ex 4 Adding Expressions With Polynomial Denominators Add 3 7 and x – 5. x+4 Step 1: Find the LCD of x + 4 and x – 5. Since there are no common factors, the LCD is (x + 4)(x – 5). Step 2: Rewrite using the LCD and add. 7 3 + = x+4 x– 5 7 (x – 5) (x + 4) (x – 5) + 7 x – 35 3 (x + 4) (x – 5) 3 x + 12 = (x + 4) (x – 5) + (x + 4) (x – 5) = 7 x – 35 + 3 x + 12 (x + 4) (x – 5) 10 x – 23 = (x + 4) (x – 5) Rewrite the fractions using the LCD. Simplify each numerator. Add the numerators. Simplify the numerator.

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