How do you evaluate \frac { 4} { x ^ { 2} - 25} + \frac { 6} { x ^ { 2} + 6x + 5}?

1 Answer
Nov 11, 2017
  1. Factor the denominators
  2. Find LCD
  3. Make equivalent fractions with Like denominators
  4. Add like Terms

(10x - 26)/((x-5)(x+5)(x+1) )

Explanation:

4/(x^2 -25) + 6/(x^2 + 6x +5)

to factor x^2-25 you need to understand difference of squares where (x-5)(x+5) = x^2 -25

4/((x-5)(x+5)) + 6/((x+1)(x+5)

our LCD is (x-5)(x+5)(x+1)

4/((x-5)(x+5)) * ((x+1))/((x+1)) = (4(x+1))/((x-5)(x+5)(x+1) and

6/((x+1)(x+5)) * ((x-5))/((x-5)) = (6(x-5))/((x-5)(x+5)(x+1))

(4(x+1) + 6(x-5))/((x-5)(x+5)(x+1) )

Distributive Property

(4x + 4 + 6x - 30)/((x-5)(x+5)(x+1) )

add like terms

(10x - 26)/((x-5)(x+5)(x+1) ) Fully simplified