Evaluate
\frac{2x^{2}-13x+7}{\left(x-1\right)\left(x^{2}-9\right)}
Expand
\frac{2x^{2}-13x+7}{\left(x-1\right)\left(x^{2}-9\right)}
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\frac{3x-1}{\left(x-1\right)\left(x+3\right)}-\frac{x+4}{\left(x-3\right)\left(x+3\right)}
Factor x^{2}+2x-3. Factor x^{2}-9.
\frac{\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}-\frac{\left(x+4\right)\left(x-1\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-1\right)\left(x+3\right) and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x-1\right)\left(x+3\right). Multiply \frac{3x-1}{\left(x-1\right)\left(x+3\right)} times \frac{x-3}{x-3}. Multiply \frac{x+4}{\left(x-3\right)\left(x+3\right)} times \frac{x-1}{x-1}.
\frac{\left(3x-1\right)\left(x-3\right)-\left(x+4\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Since \frac{\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} and \frac{\left(x+4\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-9x-x+3-x^{2}+x-4x+4}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Do the multiplications in \left(3x-1\right)\left(x-3\right)-\left(x+4\right)\left(x-1\right).
\frac{2x^{2}-13x+7}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Combine like terms in 3x^{2}-9x-x+3-x^{2}+x-4x+4.
\frac{2x^{2}-13x+7}{x^{3}-x^{2}-9x+9}
Expand \left(x-3\right)\left(x-1\right)\left(x+3\right).
\frac{3x-1}{\left(x-1\right)\left(x+3\right)}-\frac{x+4}{\left(x-3\right)\left(x+3\right)}
Factor x^{2}+2x-3. Factor x^{2}-9.
\frac{\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}-\frac{\left(x+4\right)\left(x-1\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-1\right)\left(x+3\right) and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x-1\right)\left(x+3\right). Multiply \frac{3x-1}{\left(x-1\right)\left(x+3\right)} times \frac{x-3}{x-3}. Multiply \frac{x+4}{\left(x-3\right)\left(x+3\right)} times \frac{x-1}{x-1}.
\frac{\left(3x-1\right)\left(x-3\right)-\left(x+4\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Since \frac{\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} and \frac{\left(x+4\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-9x-x+3-x^{2}+x-4x+4}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Do the multiplications in \left(3x-1\right)\left(x-3\right)-\left(x+4\right)\left(x-1\right).
\frac{2x^{2}-13x+7}{\left(x-3\right)\left(x-1\right)\left(x+3\right)}
Combine like terms in 3x^{2}-9x-x+3-x^{2}+x-4x+4.
\frac{2x^{2}-13x+7}{x^{3}-x^{2}-9x+9}
Expand \left(x-3\right)\left(x-1\right)\left(x+3\right).
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Simultaneous equation
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Differentiation
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Limits
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