Evaluate
\frac{x^{3}+7x^{2}-14x-24}{\left(x-1\right)\left(x^{2}-9\right)}
Expand
\frac{x^{3}+7x^{2}-14x-24}{\left(x-1\right)\left(x^{2}-9\right)}
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\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}+\frac{\left(x-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{x^{2}+2x-3}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x-3 is \left(x-3\right)\left(x-1\right). Multiply \frac{x+3}{x-1} times \frac{x-3}{x-3}. Multiply \frac{x-1}{x-3} times \frac{x-1}{x-1}.
\frac{\left(x+3\right)\left(x-3\right)+\left(x-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{x^{2}+2x-3}
Since \frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)} and \frac{\left(x-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}-3x+3x-9+x^{2}-x-x+1}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{x^{2}+2x-3}
Do the multiplications in \left(x+3\right)\left(x-3\right)+\left(x-1\right)\left(x-1\right).
\frac{2x^{2}-2x-8}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{x^{2}+2x-3}
Combine like terms in x^{2}-3x+3x-9+x^{2}-x-x+1.
\frac{2x^{2}-2x-8}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{\left(x-1\right)\left(x+3\right)}
Factor x^{2}+2x-3.
\frac{\left(2x^{2}-2x-8\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}-\frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x-1\right) and \left(x-1\right)\left(x+3\right) is \left(x-3\right)\left(x-1\right)\left(x+3\right). Multiply \frac{2x^{2}-2x-8}{\left(x-3\right)\left(x-1\right)} times \frac{x+3}{x+3}. Multiply \frac{x^{2}}{\left(x-1\right)\left(x+3\right)} times \frac{x-3}{x-3}.
\frac{\left(2x^{2}-2x-8\right)\left(x+3\right)-x^{2}\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Since \frac{\left(2x^{2}-2x-8\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} and \frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{3}+6x^{2}-2x^{2}-6x-8x-24-x^{3}+3x^{2}}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Do the multiplications in \left(2x^{2}-2x-8\right)\left(x+3\right)-x^{2}\left(x-3\right).
\frac{x^{3}+7x^{2}-14x-24}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Combine like terms in 2x^{3}+6x^{2}-2x^{2}-6x-8x-24-x^{3}+3x^{2}.
\frac{x^{3}+7x^{2}-14x-24}{x^{3}-x^{2}-9x+9}
Expand \left(x-3\right)\left(x-1\right)\left(x+3\right).
\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}+\frac{\left(x-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{x^{2}+2x-3}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x-3 is \left(x-3\right)\left(x-1\right). Multiply \frac{x+3}{x-1} times \frac{x-3}{x-3}. Multiply \frac{x-1}{x-3} times \frac{x-1}{x-1}.
\frac{\left(x+3\right)\left(x-3\right)+\left(x-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{x^{2}+2x-3}
Since \frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)} and \frac{\left(x-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}-3x+3x-9+x^{2}-x-x+1}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{x^{2}+2x-3}
Do the multiplications in \left(x+3\right)\left(x-3\right)+\left(x-1\right)\left(x-1\right).
\frac{2x^{2}-2x-8}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{x^{2}+2x-3}
Combine like terms in x^{2}-3x+3x-9+x^{2}-x-x+1.
\frac{2x^{2}-2x-8}{\left(x-3\right)\left(x-1\right)}-\frac{x^{2}}{\left(x-1\right)\left(x+3\right)}
Factor x^{2}+2x-3.
\frac{\left(2x^{2}-2x-8\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}-\frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x-1\right) and \left(x-1\right)\left(x+3\right) is \left(x-3\right)\left(x-1\right)\left(x+3\right). Multiply \frac{2x^{2}-2x-8}{\left(x-3\right)\left(x-1\right)} times \frac{x+3}{x+3}. Multiply \frac{x^{2}}{\left(x-1\right)\left(x+3\right)} times \frac{x-3}{x-3}.
\frac{\left(2x^{2}-2x-8\right)\left(x+3\right)-x^{2}\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Since \frac{\left(2x^{2}-2x-8\right)\left(x+3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} and \frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{3}+6x^{2}-2x^{2}-6x-8x-24-x^{3}+3x^{2}}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Do the multiplications in \left(2x^{2}-2x-8\right)\left(x+3\right)-x^{2}\left(x-3\right).
\frac{x^{3}+7x^{2}-14x-24}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Combine like terms in 2x^{3}+6x^{2}-2x^{2}-6x-8x-24-x^{3}+3x^{2}.
\frac{x^{3}+7x^{2}-14x-24}{x^{3}-x^{2}-9x+9}
Expand \left(x-3\right)\left(x-1\right)\left(x+3\right).
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