Adding & Subtracting Rational Expressions  Objective: I will add and subtract rational expressions with like denominators. I will add and subtract rational expressions 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 ) The LCD Table Using an LCD Table gives you a wonderful advantage: You can SEE the factors missing from the original products

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 Factor  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. Factor, then 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

Addition Practice