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\frac{\left(x+12\right)^{2}\left(12x-144\right)}{\left(x-12\right)\left(x^{2}-144\right)}
Divide \frac{\left(x+12\right)^{2}}{x-12} by \frac{x^{2}-144}{12x-144} by multiplying \frac{\left(x+12\right)^{2}}{x-12} by the reciprocal of \frac{x^{2}-144}{12x-144}.
\frac{12\left(x-12\right)\left(x+12\right)^{2}}{\left(x+12\right)\left(x-12\right)^{2}}
Factor the expressions that are not already factored.
\frac{12\left(x+12\right)}{x-12}
Cancel out \left(x-12\right)\left(x+12\right) in both numerator and denominator.
\frac{12x+144}{x-12}
Expand the expression.
\frac{\left(x+12\right)^{2}\left(12x-144\right)}{\left(x-12\right)\left(x^{2}-144\right)}
Divide \frac{\left(x+12\right)^{2}}{x-12} by \frac{x^{2}-144}{12x-144} by multiplying \frac{\left(x+12\right)^{2}}{x-12} by the reciprocal of \frac{x^{2}-144}{12x-144}.
\frac{12\left(x-12\right)\left(x+12\right)^{2}}{\left(x+12\right)\left(x-12\right)^{2}}
Factor the expressions that are not already factored.
\frac{12\left(x+12\right)}{x-12}
Cancel out \left(x-12\right)\left(x+12\right) in both numerator and denominator.
\frac{12x+144}{x-12}
Expand the expression.