 Section 6.3 Adding & Subtracting Rational Expressions  Adding & Subtracting RE’s with Same Denominator  Finding the LCD of 2 or more Polynomial Denominators.

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Section 6.3 Adding & Subtracting Rational Expressions  Adding & Subtracting RE’s with Same Denominator  Finding the LCD of 2 or more Polynomial Denominators  Adjusting Opposite Factors in Denominators  Adding & Subtracting RE’s with Unlike Denominators

Adding and Subtracting Fractions with Identical Denominators

Finding the LCD (monomials) (must be done before adding or subtracting 2 or more RE’s) 1. Factor each denominator completely into primes. 2. List all factors of each denominator. (use powers when duplicate factors exist) 3. The LCD is the product of each factor to its highest power. 28z 3 = (2 2 ) (7)(z 3 ) 21z = (3) (7)(z) LCD= (2 2 )(3)(7)(z 3 )

Finding the LCD (polynomials) (must be done before adding or subtracting 2 or more RE’s) 1. Factor each denominator completely into primes. 2. List all factors of each denominator. (use powers when duplicate factors exist) 3. The LCD is the product of each factor to its highest power. (a 2 – 25) = (a + 5)(a – 5) (a 2 + 7a + 10)= (a + 5) (a + 2) LCD = (a + 5)(a – 5)(a + 2)

Find the LCD (of more than 2 polynomials)  ? ? ? 8(x – 3) (x 2 – x – 6) (2x 2 – 12x + 18) 8(x – 3) = (2) 3 (x – 3) (x 2 – x – 6) = (x – 3)(x + 2) (2x 2 – 12x + 18) = (2) (x – 3) 2 LCD = (2) 3 (x – 3) 2 (x + 2)

Adjusting an Opposite Denominator  Situation: one factor is the opposite of the other  For 7 and 2 find the LCD 3(a – 2) (2 – a)  For the second expression, multiply top and bottom by -1 (this doesn’t change its value)  Now 7 and -2 find the LCD 3(a – 2) (a – 2)  Do this after factoring, before writing the LCD

1. Find the LCD. 2. Express each rational expression with a denominator that is the LCD. 3. Add (or subtract) the resulting rational expressions. 4. Simplify the result if possible. Adding or subtracting rational expressions with unlike denominators