Evaluate
-\frac{\left(x+1\right)\left(x+2\right)}{2-3x-x^{2}}
Expand
\frac{x^{2}+3x+2}{x^{2}+3x-2}
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\frac{\frac{\left(x^{2}-x-2\right)\left(x-3\right)}{\left(x^{2}-3x\right)\left(x^{2}+3x-2\right)}}{\frac{x-2}{x^{2}+2x}}
Multiply \frac{x^{2}-x-2}{x^{2}-3x} times \frac{x-3}{x^{2}+3x-2} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x^{2}-x-2\right)\left(x-3\right)\left(x^{2}+2x\right)}{\left(x^{2}-3x\right)\left(x^{2}+3x-2\right)\left(x-2\right)}
Divide \frac{\left(x^{2}-x-2\right)\left(x-3\right)}{\left(x^{2}-3x\right)\left(x^{2}+3x-2\right)} by \frac{x-2}{x^{2}+2x} by multiplying \frac{\left(x^{2}-x-2\right)\left(x-3\right)}{\left(x^{2}-3x\right)\left(x^{2}+3x-2\right)} by the reciprocal of \frac{x-2}{x^{2}+2x}.
\frac{x\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(x+2\right)}{x\left(x-3\right)\left(x-2\right)\left(x-\left(-\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)}
Factor the expressions that are not already factored.
\frac{\left(x+1\right)\left(x+2\right)}{\left(x-\left(-\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)}
Cancel out x\left(x-3\right)\left(x-2\right) in both numerator and denominator.
\frac{x^{2}+3x+2}{x^{2}+3x-2}
Expand the expression.
\frac{\frac{\left(x^{2}-x-2\right)\left(x-3\right)}{\left(x^{2}-3x\right)\left(x^{2}+3x-2\right)}}{\frac{x-2}{x^{2}+2x}}
Multiply \frac{x^{2}-x-2}{x^{2}-3x} times \frac{x-3}{x^{2}+3x-2} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x^{2}-x-2\right)\left(x-3\right)\left(x^{2}+2x\right)}{\left(x^{2}-3x\right)\left(x^{2}+3x-2\right)\left(x-2\right)}
Divide \frac{\left(x^{2}-x-2\right)\left(x-3\right)}{\left(x^{2}-3x\right)\left(x^{2}+3x-2\right)} by \frac{x-2}{x^{2}+2x} by multiplying \frac{\left(x^{2}-x-2\right)\left(x-3\right)}{\left(x^{2}-3x\right)\left(x^{2}+3x-2\right)} by the reciprocal of \frac{x-2}{x^{2}+2x}.
\frac{x\left(x-3\right)\left(x-2\right)\left(x+1\right)\left(x+2\right)}{x\left(x-3\right)\left(x-2\right)\left(x-\left(-\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)}
Factor the expressions that are not already factored.
\frac{\left(x+1\right)\left(x+2\right)}{\left(x-\left(-\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}-\frac{3}{2}\right)\right)}
Cancel out x\left(x-3\right)\left(x-2\right) in both numerator and denominator.
\frac{x^{2}+3x+2}{x^{2}+3x-2}
Expand the expression.
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Limits
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