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\frac{\left(x^{2}-1\right)\left(12-6x\right)}{\left(x-2\right)\left(x+1\right)}
Divide \frac{x^{2}-1}{x-2} by \frac{x+1}{12-6x} by multiplying \frac{x^{2}-1}{x-2} by the reciprocal of \frac{x+1}{12-6x}.
\frac{6\left(x-1\right)\left(x+1\right)\left(-x+2\right)}{\left(x-2\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{-6\left(x-2\right)\left(x-1\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}
Extract the negative sign in 2-x.
-6\left(x-1\right)
Cancel out \left(x-2\right)\left(x+1\right) in both numerator and denominator.
-6x+6
Expand the expression.
\frac{\left(x^{2}-1\right)\left(12-6x\right)}{\left(x-2\right)\left(x+1\right)}
Divide \frac{x^{2}-1}{x-2} by \frac{x+1}{12-6x} by multiplying \frac{x^{2}-1}{x-2} by the reciprocal of \frac{x+1}{12-6x}.
\frac{6\left(x-1\right)\left(x+1\right)\left(-x+2\right)}{\left(x-2\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{-6\left(x-2\right)\left(x-1\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}
Extract the negative sign in 2-x.
-6\left(x-1\right)
Cancel out \left(x-2\right)\left(x+1\right) in both numerator and denominator.
-6x+6
Expand the expression.