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\frac{\left(x^{2}-7x+6\right)\left(x^{2}-16\right)}{\left(x+4\right)\left(x-1\right)^{2}}
Divide \frac{x^{2}-7x+6}{x+4} by \frac{\left(x-1\right)^{2}}{x^{2}-16} by multiplying \frac{x^{2}-7x+6}{x+4} by the reciprocal of \frac{\left(x-1\right)^{2}}{x^{2}-16}.
\frac{\left(x-6\right)\left(x-4\right)\left(x-1\right)\left(x+4\right)}{\left(x+4\right)\left(x-1\right)^{2}}
Factor the expressions that are not already factored.
\frac{\left(x-6\right)\left(x-4\right)}{x-1}
Cancel out \left(x-1\right)\left(x+4\right) in both numerator and denominator.
\frac{x^{2}-10x+24}{x-1}
Expand the expression.
\frac{\left(x^{2}-7x+6\right)\left(x^{2}-16\right)}{\left(x+4\right)\left(x-1\right)^{2}}
Divide \frac{x^{2}-7x+6}{x+4} by \frac{\left(x-1\right)^{2}}{x^{2}-16} by multiplying \frac{x^{2}-7x+6}{x+4} by the reciprocal of \frac{\left(x-1\right)^{2}}{x^{2}-16}.
\frac{\left(x-6\right)\left(x-4\right)\left(x-1\right)\left(x+4\right)}{\left(x+4\right)\left(x-1\right)^{2}}
Factor the expressions that are not already factored.
\frac{\left(x-6\right)\left(x-4\right)}{x-1}
Cancel out \left(x-1\right)\left(x+4\right) in both numerator and denominator.
\frac{x^{2}-10x+24}{x-1}
Expand the expression.