Question

How do you combine `x / (x^2-4) + (3x - 5) /(x^2 + 4x + 4)`?

Answer 1

In order to create a common denominator note that
`(x^2-4)(x+2) = (x-2)(x+2)(x+2) = (x-2)(x^2+4x+4)`

So
`x/(x^2-4) + (3x-5)/(x^2+4x+4)`

`=(x(x+2) +(3x-5)(x-2))/((x-2)(x+2)(x+2))`

`= (x^2+2x +3x^2-11x+15)/((x-2)(x+2)(x+2))`

`=(4x^2-9x+15)/(x^3+2x^2-4x-8)`