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