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