Question

How do I solve this

Answer 1

$\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ \cfrac{2x}{x^2+2x-24}-\cfrac{x}{x^2-36}\quad \begin{cases} x^2+2x-24\implies (x+6)(x-4)\\ --------------\\ x^2-36\implies x^2-6^2\\ (x-6)(x+6) \end{cases}$

$\bf \cfrac{2x}{(x+6)(x-4)}-\cfrac{x}{(x-6)(x+6)}\impliedby \begin{array}{llll} \textit{thus our LCD is}\\ (x-6)(x+6)(x-4) \end{array} \\\\\\ \cfrac{[(x-6)2x]~-~[(x-4)x]}{(x-6)(x+6)(x-4)}\implies \cfrac{2x^2-12x-x^2+4x}{(x-6)(x+6)(x-4)} \\\\\\ \cfrac{x^2-8x}{(x-6)(x+6)(x-4)}$