Evaluate
\frac{x^{2}-2x-1}{x^{2}-16}
Expand
\frac{x^{2}-2x-1}{x^{2}-16}
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\frac{x+2}{x+4}+\frac{7}{\left(x-4\right)\left(x+4\right)}
Factor x^{2}-16.
\frac{\left(x+2\right)\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}+\frac{7}{\left(x-4\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+4 and \left(x-4\right)\left(x+4\right) is \left(x-4\right)\left(x+4\right). Multiply \frac{x+2}{x+4} times \frac{x-4}{x-4}.
\frac{\left(x+2\right)\left(x-4\right)+7}{\left(x-4\right)\left(x+4\right)}
Since \frac{\left(x+2\right)\left(x-4\right)}{\left(x-4\right)\left(x+4\right)} and \frac{7}{\left(x-4\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}-4x+2x-8+7}{\left(x-4\right)\left(x+4\right)}
Do the multiplications in \left(x+2\right)\left(x-4\right)+7.
\frac{x^{2}-2x-1}{\left(x-4\right)\left(x+4\right)}
Combine like terms in x^{2}-4x+2x-8+7.
\frac{x^{2}-2x-1}{x^{2}-16}
Expand \left(x-4\right)\left(x+4\right).
\frac{x+2}{x+4}+\frac{7}{\left(x-4\right)\left(x+4\right)}
Factor x^{2}-16.
\frac{\left(x+2\right)\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}+\frac{7}{\left(x-4\right)\left(x+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+4 and \left(x-4\right)\left(x+4\right) is \left(x-4\right)\left(x+4\right). Multiply \frac{x+2}{x+4} times \frac{x-4}{x-4}.
\frac{\left(x+2\right)\left(x-4\right)+7}{\left(x-4\right)\left(x+4\right)}
Since \frac{\left(x+2\right)\left(x-4\right)}{\left(x-4\right)\left(x+4\right)} and \frac{7}{\left(x-4\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}-4x+2x-8+7}{\left(x-4\right)\left(x+4\right)}
Do the multiplications in \left(x+2\right)\left(x-4\right)+7.
\frac{x^{2}-2x-1}{\left(x-4\right)\left(x+4\right)}
Combine like terms in x^{2}-4x+2x-8+7.
\frac{x^{2}-2x-1}{x^{2}-16}
Expand \left(x-4\right)\left(x+4\right).
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