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\frac{2-2a}{1-a^{2}}
Since \frac{2}{1-a^{2}} and \frac{2a}{1-a^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{2\left(-a+1\right)}{\left(a-1\right)\left(-a-1\right)}
Factor the expressions that are not already factored in \frac{2-2a}{1-a^{2}}.
\frac{-2\left(a-1\right)}{\left(a-1\right)\left(-a-1\right)}
Extract the negative sign in 1-a.
\frac{-2}{-a-1}
Cancel out a-1 in both numerator and denominator.