Evaluate
\frac{14x+9}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}
Expand
\frac{14x+9}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}
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\frac{x+3}{\left(x-8\right)\left(x+4\right)}-\frac{x}{\left(x+3\right)\left(x+4\right)}
Factor x^{2}-4x-32. Factor x^{2}+7x+12.
\frac{\left(x+3\right)\left(x+3\right)}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}-\frac{x\left(x-8\right)}{\left(x-8\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-8\right)\left(x+4\right) and \left(x+3\right)\left(x+4\right) is \left(x-8\right)\left(x+3\right)\left(x+4\right). Multiply \frac{x+3}{\left(x-8\right)\left(x+4\right)} times \frac{x+3}{x+3}. Multiply \frac{x}{\left(x+3\right)\left(x+4\right)} times \frac{x-8}{x-8}.
\frac{\left(x+3\right)\left(x+3\right)-x\left(x-8\right)}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}
Since \frac{\left(x+3\right)\left(x+3\right)}{\left(x-8\right)\left(x+3\right)\left(x+4\right)} and \frac{x\left(x-8\right)}{\left(x-8\right)\left(x+3\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+3x+3x+9-x^{2}+8x}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}
Do the multiplications in \left(x+3\right)\left(x+3\right)-x\left(x-8\right).
\frac{14x+9}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}
Combine like terms in x^{2}+3x+3x+9-x^{2}+8x.
\frac{14x+9}{x^{3}-x^{2}-44x-96}
Expand \left(x-8\right)\left(x+3\right)\left(x+4\right).
\frac{x+3}{\left(x-8\right)\left(x+4\right)}-\frac{x}{\left(x+3\right)\left(x+4\right)}
Factor x^{2}-4x-32. Factor x^{2}+7x+12.
\frac{\left(x+3\right)\left(x+3\right)}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}-\frac{x\left(x-8\right)}{\left(x-8\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-8\right)\left(x+4\right) and \left(x+3\right)\left(x+4\right) is \left(x-8\right)\left(x+3\right)\left(x+4\right). Multiply \frac{x+3}{\left(x-8\right)\left(x+4\right)} times \frac{x+3}{x+3}. Multiply \frac{x}{\left(x+3\right)\left(x+4\right)} times \frac{x-8}{x-8}.
\frac{\left(x+3\right)\left(x+3\right)-x\left(x-8\right)}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}
Since \frac{\left(x+3\right)\left(x+3\right)}{\left(x-8\right)\left(x+3\right)\left(x+4\right)} and \frac{x\left(x-8\right)}{\left(x-8\right)\left(x+3\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+3x+3x+9-x^{2}+8x}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}
Do the multiplications in \left(x+3\right)\left(x+3\right)-x\left(x-8\right).
\frac{14x+9}{\left(x-8\right)\left(x+3\right)\left(x+4\right)}
Combine like terms in x^{2}+3x+3x+9-x^{2}+8x.
\frac{14x+9}{x^{3}-x^{2}-44x-96}
Expand \left(x-8\right)\left(x+3\right)\left(x+4\right).
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