Question

Dividing rational expressions

Answer 1

$\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -----------------------------\\\\ \cfrac{x+3}{x^2-2x}\cdot \cfrac{(x-2)^2}{x^2-9}\implies \cfrac{x+3}{x^2-2x}\cdot \cfrac{(x-2)(x-2)}{x^2-3^2} \\\\\\ \cfrac{x+3}{x(x-2)}\cdot \cfrac{(x-2)(x-2)}{x^2-3^2}\implies \cfrac{\underline{x+3}}{x\underline{(x-2)}}\cdot \cfrac{\underline{(x-2)}(x-2)}{(x-3)\underline{(x+3)}} \\\\\\ \cfrac{x-2}{x(x-3)}\iff\cfrac{x-2}{x^2-3x}$