Question

How do you simplify `x/(x^2-9) - x/(x^2+6x+9)`?

Answer 1

`(6x)/(x^3+3x^2-9x-27)`

Explanation:

Factoring:
`color(white)("XXX")x^2-9 = (x+3)(x-3)`
`color(white)("XXX")x^2+6x+9 = (x+3)(x+3)`

`x/(x^2-9) - x/(x^2+6x+9)`

`color(white)("XXX")=(x(x+3)-x(x-3))/((x+3)(x+3)(x-3))`

`color(white)("XXX")=(6x)/(x^3+3x^2-9x-27)`