Section 6.2 Adding & Subtracting Rational Expressions  Adding & Subtracting Rational Expressions with the Same Denominators  Finding the LCD of 2 or more Polynomial Denominators  Adjusting Opposite Factors in Denominators  Adding & Subtracting Rational Expressions with Unlike Denominators  1 1 ?  =

Adding and Subtracting Fractions with Identical Denominators Perform the operation : 6.22

Finding the LCD (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 ) 3 21z = (3)(7) (z) 4z 2 LCD= (2 2 )(3)(7)(z 3 ) Lacks↑ (a 2 – 25) = (a + 5)(a – 5) (a + 2) (a + 7a + 10) = (a + 5) (a + 2) (a – 5) LCD = (a + 5)(a – 5)(a + 2) Lacks↑ 6.23

 ? ? ? 8(x – 3) (x 2 – x – 6) (2x 2 – 12x + 18) 8(x – 3) = (2) 3 (x – 3) (x + 2)(x – 3) (x 2 – x – 6) = (x – 3)(x + 2) 8(x – 3) (2x 2 – 12x + 18) = (2) (x – 3) 2 4(x + 2) LCD = (2) 3 (x – 3) 2 (x + 2) Lacks↑ Find the LCD, using a Primes Table 6.24

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 (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 6.25

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 – note any exclusions Exclusions: a ≠ ±2 6.26

Add & Subtract Practice - monomials Exclusions: x ≠

Add & Subtract Practice - simplifying 6.28

Add & Subtract Practice – change both Exclusions: y ≠ ±1,

Brain Break: 6.210

Add & Subtract – opposite monomials Exclusions: a ≠

Add & Subtract – opposite binomials

Add & Subtract – function simplification Exclusions: x ≠ ±

What Next?  6.3 Complex Fractions next time