Evaluate
-\frac{\left(x+6\right)\left(x+7\right)}{14-3x-x^{2}}
Expand
\frac{x^{2}+13x+42}{x^{2}+3x-14}
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\frac{\left(x^{2}+9x+14\right)\left(x^{2}+3x-18\right)}{\left(x^{2}-x-6\right)\left(x^{2}+3x-14\right)}
Divide \frac{x^{2}+9x+14}{x^{2}-x-6} by \frac{x^{2}+3x-14}{x^{2}+3x-18} by multiplying \frac{x^{2}+9x+14}{x^{2}-x-6} by the reciprocal of \frac{x^{2}+3x-14}{x^{2}+3x-18}.
\frac{\left(x-3\right)\left(x+2\right)\left(x+6\right)\left(x+7\right)}{\left(x-3\right)\left(x+2\right)\left(x-\left(-\frac{1}{2}\sqrt{65}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{65}-\frac{3}{2}\right)\right)}
Factor the expressions that are not already factored.
\frac{\left(x+6\right)\left(x+7\right)}{\left(x-\left(-\frac{1}{2}\sqrt{65}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{65}-\frac{3}{2}\right)\right)}
Cancel out \left(x-3\right)\left(x+2\right) in both numerator and denominator.
\frac{x^{2}+13x+42}{x^{2}+3x-14}
Expand the expression.
\frac{\left(x^{2}+9x+14\right)\left(x^{2}+3x-18\right)}{\left(x^{2}-x-6\right)\left(x^{2}+3x-14\right)}
Divide \frac{x^{2}+9x+14}{x^{2}-x-6} by \frac{x^{2}+3x-14}{x^{2}+3x-18} by multiplying \frac{x^{2}+9x+14}{x^{2}-x-6} by the reciprocal of \frac{x^{2}+3x-14}{x^{2}+3x-18}.
\frac{\left(x-3\right)\left(x+2\right)\left(x+6\right)\left(x+7\right)}{\left(x-3\right)\left(x+2\right)\left(x-\left(-\frac{1}{2}\sqrt{65}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{65}-\frac{3}{2}\right)\right)}
Factor the expressions that are not already factored.
\frac{\left(x+6\right)\left(x+7\right)}{\left(x-\left(-\frac{1}{2}\sqrt{65}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{65}-\frac{3}{2}\right)\right)}
Cancel out \left(x-3\right)\left(x+2\right) in both numerator and denominator.
\frac{x^{2}+13x+42}{x^{2}+3x-14}
Expand the expression.
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