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\frac{\left(x-1\right)\left(2x-1\right)^{2}}{x\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{\left(2x-1\right)^{2}}{x\left(x+1\right)}
Cancel out x-1 in both numerator and denominator.
\frac{4x^{2}-4x+1}{x^{2}+x}
Expand the expression.
\frac{\left(x-1\right)\left(2x-1\right)^{2}}{x\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{\left(2x-1\right)^{2}}{x\left(x+1\right)}
Cancel out x-1 in both numerator and denominator.
\frac{4x^{2}-4x+1}{x^{2}+x}
Expand the expression.