Answer
$\frac{x+3}{x-4}$
Work Step by Step
To divide the fractions, take the reciprocal of the second term. Then factor both terms and multiply them together. Next, divide to simplify further.
$\frac{x^2-5x-24}{x^2-x-12}\div\frac{x^2-10x+16}{x^2+x-6}$
$\frac{x^2-5x-24}{x^2-x-12}\times\frac{x^2+x-6}{x^2-10x+16}$
$\frac{x(x+3)-8(x+3)}{x(x-4)+3(x-4)}\times\frac{x(x+3)-2(x+3)}{x(x-2)-8(x-2)}$
$\frac{(x+3)(x-8)}{(x-4)(x+3)}\times\frac{(x+3)(x-2)}{(x-2)(x-8)}$
$\frac{x+3}{x-4}$
