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\frac{\left(x^{2}-25\right)x}{x\left(x-5\right)^{2}}
Divide \frac{x^{2}-25}{x} by \frac{\left(x-5\right)^{2}}{x} by multiplying \frac{x^{2}-25}{x} by the reciprocal of \frac{\left(x-5\right)^{2}}{x}.
\frac{x^{2}-25}{\left(x-5\right)^{2}}
Cancel out x in both numerator and denominator.
\frac{\left(x-5\right)\left(x+5\right)}{\left(x-5\right)^{2}}
Factor the expressions that are not already factored.
\frac{x+5}{x-5}
Cancel out x-5 in both numerator and denominator.
\frac{\left(x^{2}-25\right)x}{x\left(x-5\right)^{2}}
Divide \frac{x^{2}-25}{x} by \frac{\left(x-5\right)^{2}}{x} by multiplying \frac{x^{2}-25}{x} by the reciprocal of \frac{\left(x-5\right)^{2}}{x}.
\frac{x^{2}-25}{\left(x-5\right)^{2}}
Cancel out x in both numerator and denominator.
\frac{\left(x-5\right)\left(x+5\right)}{\left(x-5\right)^{2}}
Factor the expressions that are not already factored.
\frac{x+5}{x-5}
Cancel out x-5 in both numerator and denominator.