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\frac{1}{x-1}\left(x^{2}-1\right)
Anything divided by one gives itself.
\frac{x^{2}-1}{x-1}
Express \frac{1}{x-1}\left(x^{2}-1\right) as a single fraction.
\frac{\left(x-1\right)\left(x+1\right)}{x-1}
Factor the expressions that are not already factored.
x+1
Cancel out x-1 in both numerator and denominator.
\frac{1}{x-1}\left(x^{2}-1\right)
Anything divided by one gives itself.
\frac{x^{2}-1}{x-1}
Express \frac{1}{x-1}\left(x^{2}-1\right) as a single fraction.
\frac{\left(x-1\right)\left(x+1\right)}{x-1}
Factor the expressions that are not already factored.
x+1
Cancel out x-1 in both numerator and denominator.