Evaluate
\frac{-2x^{2}+14x-3}{\left(x+4\right)\left(x^{2}-9\right)}
Expand
\frac{-2x^{2}+14x-3}{\left(x+4\right)\left(x^{2}-9\right)}
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\frac{x}{\left(x-3\right)\left(x+3\right)}-\frac{3x-1}{\left(x+3\right)\left(x+4\right)}
Factor x^{2}-9. Factor x^{2}+7x+12.
\frac{x\left(x+4\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}-\frac{\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right) and \left(x+3\right)\left(x+4\right) is \left(x-3\right)\left(x+3\right)\left(x+4\right). Multiply \frac{x}{\left(x-3\right)\left(x+3\right)} times \frac{x+4}{x+4}. Multiply \frac{3x-1}{\left(x+3\right)\left(x+4\right)} times \frac{x-3}{x-3}.
\frac{x\left(x+4\right)-\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Since \frac{x\left(x+4\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)} and \frac{\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+4x-3x^{2}+9x+x-3}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Do the multiplications in x\left(x+4\right)-\left(3x-1\right)\left(x-3\right).
\frac{-2x^{2}+14x-3}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Combine like terms in x^{2}+4x-3x^{2}+9x+x-3.
\frac{-2x^{2}+14x-3}{x^{3}+4x^{2}-9x-36}
Expand \left(x-3\right)\left(x+3\right)\left(x+4\right).
\frac{x}{\left(x-3\right)\left(x+3\right)}-\frac{3x-1}{\left(x+3\right)\left(x+4\right)}
Factor x^{2}-9. Factor x^{2}+7x+12.
\frac{x\left(x+4\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}-\frac{\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right) and \left(x+3\right)\left(x+4\right) is \left(x-3\right)\left(x+3\right)\left(x+4\right). Multiply \frac{x}{\left(x-3\right)\left(x+3\right)} times \frac{x+4}{x+4}. Multiply \frac{3x-1}{\left(x+3\right)\left(x+4\right)} times \frac{x-3}{x-3}.
\frac{x\left(x+4\right)-\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Since \frac{x\left(x+4\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)} and \frac{\left(3x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+4x-3x^{2}+9x+x-3}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Do the multiplications in x\left(x+4\right)-\left(3x-1\right)\left(x-3\right).
\frac{-2x^{2}+14x-3}{\left(x-3\right)\left(x+3\right)\left(x+4\right)}
Combine like terms in x^{2}+4x-3x^{2}+9x+x-3.
\frac{-2x^{2}+14x-3}{x^{3}+4x^{2}-9x-36}
Expand \left(x-3\right)\left(x+3\right)\left(x+4\right).
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