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\frac{\left(x-1\right)\left(x^{2}-x-12\right)}{\left(x^{2}-3x-4\right)\left(x^{2}+x-2\right)}
Divide \frac{x-1}{x^{2}-3x-4} by \frac{x^{2}+x-2}{x^{2}-x-12} by multiplying \frac{x-1}{x^{2}-3x-4} by the reciprocal of \frac{x^{2}+x-2}{x^{2}-x-12}.
\frac{\left(x-4\right)\left(x-1\right)\left(x+3\right)}{\left(x-4\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)}
Factor the expressions that are not already factored.
\frac{x+3}{\left(x+1\right)\left(x+2\right)}
Cancel out \left(x-4\right)\left(x-1\right) in both numerator and denominator.
\frac{x+3}{x^{2}+3x+2}
Expand the expression.
\frac{\left(x-1\right)\left(x^{2}-x-12\right)}{\left(x^{2}-3x-4\right)\left(x^{2}+x-2\right)}
Divide \frac{x-1}{x^{2}-3x-4} by \frac{x^{2}+x-2}{x^{2}-x-12} by multiplying \frac{x-1}{x^{2}-3x-4} by the reciprocal of \frac{x^{2}+x-2}{x^{2}-x-12}.
\frac{\left(x-4\right)\left(x-1\right)\left(x+3\right)}{\left(x-4\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)}
Factor the expressions that are not already factored.
\frac{x+3}{\left(x+1\right)\left(x+2\right)}
Cancel out \left(x-4\right)\left(x-1\right) in both numerator and denominator.
\frac{x+3}{x^{2}+3x+2}
Expand the expression.