Question

Simplify the equation and write the answer without negative exponents

Answer 1

$\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------$

$\bf \cfrac{x^2}{x^2-4}-\cfrac{x+1}{x+2}\implies \cfrac{x^2}{x^2-2^2}-\cfrac{x+1}{x+2}\implies \cfrac{x^2}{(x-2)(x+2)}-\cfrac{x+1}{x+2} \\\\\\ \textit{so, then the LCD will just be }(x-2)(x+2) \\\\\\ \cfrac{x^2-(x+1)(x-2)}{(x-2)(x+2)}\implies \cfrac{x^2-(x^2-x-2)}{(x-2)(x+2)}\implies \cfrac{\underline{x^2-x^2}+x+2}{(x-2)(x+2)} \\\\\\ \cfrac{\underline{x+2}}{(x-2)\underline{(x+2)}}\implies \cfrac{1}{x-2}$