Question

Find the sum. Write your answer in the simplest form. Show your work

Answer 1

`((x+4))/(x(x+2))`

Explanation:

`(x-4)/(x^2-2x) + (4)/(x^2-4)`

Start by factorizing the denominators of both the terms to get:

`(x-4)/(x(x-2)) + (4)/((x+2)(x-2))`

Now take the LCM for both the terms to get:

`((x-4)(x-2))/(x(x-2)(x+2)) + (4x)/((x-2)(x-2)x)`

Combine the fractions to get:

`((x-4)(x-2)+4x)/(x(x-2)(x+2))`

Factor 4x + (x - 4) (x + 2) to get:

`((x-2)(x+4))/(x(x-2)(x+2))`

Cancelling the term (x - 2) to get the sum:

`((x+4))/(x(x+2))`