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\frac{\left(x+4\right)\left(x^{2}-5x-24\right)}{\left(x-8\right)\left(x+6\right)}
Divide \frac{x+4}{x-8} by \frac{x+6}{x^{2}-5x-24} by multiplying \frac{x+4}{x-8} by the reciprocal of \frac{x+6}{x^{2}-5x-24}.
\frac{\left(x-8\right)\left(x+3\right)\left(x+4\right)}{\left(x-8\right)\left(x+6\right)}
Factor the expressions that are not already factored.
\frac{\left(x+3\right)\left(x+4\right)}{x+6}
Cancel out x-8 in both numerator and denominator.
\frac{x^{2}+7x+12}{x+6}
Expand the expression.
\frac{\left(x+4\right)\left(x^{2}-5x-24\right)}{\left(x-8\right)\left(x+6\right)}
Divide \frac{x+4}{x-8} by \frac{x+6}{x^{2}-5x-24} by multiplying \frac{x+4}{x-8} by the reciprocal of \frac{x+6}{x^{2}-5x-24}.
\frac{\left(x-8\right)\left(x+3\right)\left(x+4\right)}{\left(x-8\right)\left(x+6\right)}
Factor the expressions that are not already factored.
\frac{\left(x+3\right)\left(x+4\right)}{x+6}
Cancel out x-8 in both numerator and denominator.
\frac{x^{2}+7x+12}{x+6}
Expand the expression.