Evaluate
\frac{9}{\left(x-2\right)\left(x+1\right)}
Expand
\frac{9}{\left(x-2\right)\left(x+1\right)}
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\frac{\left(x^{2}+1-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{\left(x^{2}+4+2x\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and 1+x is \left(x-2\right)\left(x+1\right). Multiply \frac{x^{2}+1-x}{x-2} times \frac{x+1}{x+1}. Multiply \frac{x^{2}+4+2x}{1+x} times \frac{x-2}{x-2}.
\frac{\left(x^{2}+1-x\right)\left(x+1\right)-\left(x^{2}+4+2x\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
Since \frac{\left(x^{2}+1-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} and \frac{\left(x^{2}+4+2x\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}+x^{2}+1+x-x^{2}-x-x^{3}+2x^{2}-4x+8-2x^{2}+4x}{\left(x-2\right)\left(x+1\right)}
Do the multiplications in \left(x^{2}+1-x\right)\left(x+1\right)-\left(x^{2}+4+2x\right)\left(x-2\right).
\frac{9}{\left(x-2\right)\left(x+1\right)}
Combine like terms in x^{3}+x^{2}+1+x-x^{2}-x-x^{3}+2x^{2}-4x+8-2x^{2}+4x.
\frac{9}{x^{2}-x-2}
Expand \left(x-2\right)\left(x+1\right).
\frac{\left(x^{2}+1-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{\left(x^{2}+4+2x\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and 1+x is \left(x-2\right)\left(x+1\right). Multiply \frac{x^{2}+1-x}{x-2} times \frac{x+1}{x+1}. Multiply \frac{x^{2}+4+2x}{1+x} times \frac{x-2}{x-2}.
\frac{\left(x^{2}+1-x\right)\left(x+1\right)-\left(x^{2}+4+2x\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
Since \frac{\left(x^{2}+1-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} and \frac{\left(x^{2}+4+2x\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}+x^{2}+1+x-x^{2}-x-x^{3}+2x^{2}-4x+8-2x^{2}+4x}{\left(x-2\right)\left(x+1\right)}
Do the multiplications in \left(x^{2}+1-x\right)\left(x+1\right)-\left(x^{2}+4+2x\right)\left(x-2\right).
\frac{9}{\left(x-2\right)\left(x+1\right)}
Combine like terms in x^{3}+x^{2}+1+x-x^{2}-x-x^{3}+2x^{2}-4x+8-2x^{2}+4x.
\frac{9}{x^{2}-x-2}
Expand \left(x-2\right)\left(x+1\right).
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