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\frac{14x^{2}\left(x^{2}-2x+1\right)}{\left(x+1\right)\left(x^{2}-x\right)}
Divide \frac{14x^{2}}{x+1} by \frac{x^{2}-x}{x^{2}-2x+1} by multiplying \frac{14x^{2}}{x+1} by the reciprocal of \frac{x^{2}-x}{x^{2}-2x+1}.
\frac{14x^{2}\left(x-1\right)^{2}}{x\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{14x\left(x-1\right)}{x+1}
Cancel out x\left(x-1\right) in both numerator and denominator.
\frac{14x^{2}-14x}{x+1}
Expand the expression.
\frac{14x^{2}\left(x^{2}-2x+1\right)}{\left(x+1\right)\left(x^{2}-x\right)}
Divide \frac{14x^{2}}{x+1} by \frac{x^{2}-x}{x^{2}-2x+1} by multiplying \frac{14x^{2}}{x+1} by the reciprocal of \frac{x^{2}-x}{x^{2}-2x+1}.
\frac{14x^{2}\left(x-1\right)^{2}}{x\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{14x\left(x-1\right)}{x+1}
Cancel out x\left(x-1\right) in both numerator and denominator.
\frac{14x^{2}-14x}{x+1}
Expand the expression.