Question

Simplify 1/(x^2-4) - 1/(x^3-8)

I have checked through wolfram and got the answer but I would like help with the steps.

Answer 1

\[\frac{1}{x^2-4}-\frac{1}{x^3-8}=\frac{1}{(x+2)(x-2)}-\frac{1}{(x-2)(x^2+2x+4)}\]\[=\frac{x^2+2x+4-(x+2)}{(x+2)(x-2)(x^2+2x+4)}\]\[=\frac{x^2+x+2}{(x+2)(x-2)(x^2+2x+4)}\]

Answer 2

Thanks, thats exactly what I was looking for.