Evaluate
\frac{\left(x-3\right)x^{2}}{x^{2}-1}
Expand
\frac{x^{3}-3x^{2}}{x^{2}-1}
Graph
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x-3+\frac{x-3}{\left(x-1\right)\left(x+1\right)}
Factor x^{2}-1.
\frac{\left(x-3\right)\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{x-3}{\left(x-1\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply x-3 times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{\left(x-3\right)\left(x-1\right)\left(x+1\right)+x-3}{\left(x-1\right)\left(x+1\right)}
Since \frac{\left(x-3\right)\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{x-3}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{3}-x-3x^{2}+3+x-3}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in \left(x-3\right)\left(x-1\right)\left(x+1\right)+x-3.
\frac{x^{3}-3x^{2}}{\left(x-1\right)\left(x+1\right)}
Combine like terms in x^{3}-x-3x^{2}+3+x-3.
\frac{x^{3}-3x^{2}}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
x-3+\frac{x-3}{\left(x-1\right)\left(x+1\right)}
Factor x^{2}-1.
\frac{\left(x-3\right)\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{x-3}{\left(x-1\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply x-3 times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{\left(x-3\right)\left(x-1\right)\left(x+1\right)+x-3}{\left(x-1\right)\left(x+1\right)}
Since \frac{\left(x-3\right)\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{x-3}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{3}-x-3x^{2}+3+x-3}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in \left(x-3\right)\left(x-1\right)\left(x+1\right)+x-3.
\frac{x^{3}-3x^{2}}{\left(x-1\right)\left(x+1\right)}
Combine like terms in x^{3}-x-3x^{2}+3+x-3.
\frac{x^{3}-3x^{2}}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
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Limits
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