## Precalculus: Mathematics for Calculus, 7th Edition

$x$
$\frac{x^2-x-6}{x^2+2x}\times\frac{x^3+x^2}{x^2-2x-3}$ Factorise the fraction $\frac{x^2-x-6}{x^2+2x}$: $=\frac{(x-3)(x+2)}{x(x+2)}$ Simplify the fraction: $=\frac{x-3}{x}$ Factorise the fraction $\frac{x^3+x^2}{x^2-2x-3}$: $=\frac{x^2(x+1)}{(x-3)(x+1)}$ Simplify the fraction: $=\frac{x^2}{(x-3)}$ Multiply the two results: $=\frac{x-3}{x}\times\frac{x^2}{(x-3)}$ $=\frac{x^2(x-3)}{x(x-3)}$ Cancel out $x-3$: $=\frac{x^2}{x}$ Simplify the fraction: $=x$