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\frac{\left(x^{2}-16\right)x}{\left(4x+16\right)\left(x-4\right)}
Divide \frac{x^{2}-16}{4x+16} by \frac{x-4}{x} by multiplying \frac{x^{2}-16}{4x+16} by the reciprocal of \frac{x-4}{x}.
\frac{x\left(x-4\right)\left(x+4\right)}{4\left(x-4\right)\left(x+4\right)}
Factor the expressions that are not already factored.
\frac{x}{4}
Cancel out \left(x-4\right)\left(x+4\right) in both numerator and denominator.
\frac{\left(x^{2}-16\right)x}{\left(4x+16\right)\left(x-4\right)}
Divide \frac{x^{2}-16}{4x+16} by \frac{x-4}{x} by multiplying \frac{x^{2}-16}{4x+16} by the reciprocal of \frac{x-4}{x}.
\frac{x\left(x-4\right)\left(x+4\right)}{4\left(x-4\right)\left(x+4\right)}
Factor the expressions that are not already factored.
\frac{x}{4}
Cancel out \left(x-4\right)\left(x+4\right) in both numerator and denominator.