$$\frac{x+6}{x-3}\times\frac{x^{2}+2x-8}{x^{2}+10x+24}$$
$\frac{x-2}{x-3}$
$$\frac{x+6}{x-3}\times \frac{\left(x-2\right)\left(x+4\right)}{\left(x+4\right)\left(x+6\right)}$$
$$\frac{x+6}{x-3}\times \frac{x-2}{x+6}$$
$$\frac{\left(x+6\right)\left(x-2\right)}{\left(x-3\right)\left(x+6\right)}$$
$$\frac{x-2}{x-3}$$
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