Question

Divide. Express the quotient in simplest form.

Answer 1

$( \frac{x^2 - x -12}{2x} )$ ÷ $( \frac{x^2 - 2x - 8}{4x^2} )$

= $( \frac{x^2 - x -12}{2x} )$ × $( \frac{4x^2}{x^2 - 2x - 8} )$

= $\frac{x(x^2 - x -12)}{x^2 - 2x - 8}$

= $\frac{x(x^2 -4x +3x -12)}{x^2 -4x +2x -8}$

= $\frac{x[x(x - 4) +3(x - 4)]}{x(x - 4) +2(x - 4)}$

= $\frac{x(x-4)(x+3)}{(x-4)(x+2)}$

= $\frac{x(x+3)}{(x+2)}$