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\frac{4}{x^{2}-64}
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\frac{4}{x^{2}-64}
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\frac{x-2}{\left(x-8\right)\left(x+8\right)}-\frac{6-x}{\left(x-8\right)\left(-x-8\right)}
Factor x^{2}-64. Factor 64-x^{2}.
\frac{x-2}{\left(x-8\right)\left(x+8\right)}-\frac{-\left(6-x\right)}{\left(x-8\right)\left(x+8\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-8\right)\left(x+8\right) and \left(x-8\right)\left(-x-8\right) is \left(x-8\right)\left(x+8\right). Multiply \frac{6-x}{\left(x-8\right)\left(-x-8\right)} times \frac{-1}{-1}.
\frac{x-2-\left(-\left(6-x\right)\right)}{\left(x-8\right)\left(x+8\right)}
Since \frac{x-2}{\left(x-8\right)\left(x+8\right)} and \frac{-\left(6-x\right)}{\left(x-8\right)\left(x+8\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x-2+6-x}{\left(x-8\right)\left(x+8\right)}
Do the multiplications in x-2-\left(-\left(6-x\right)\right).
\frac{4}{\left(x-8\right)\left(x+8\right)}
Combine like terms in x-2+6-x.
\frac{4}{x^{2}-64}
Expand \left(x-8\right)\left(x+8\right).
\frac{x-2}{\left(x-8\right)\left(x+8\right)}-\frac{6-x}{\left(x-8\right)\left(-x-8\right)}
Factor x^{2}-64. Factor 64-x^{2}.
\frac{x-2}{\left(x-8\right)\left(x+8\right)}-\frac{-\left(6-x\right)}{\left(x-8\right)\left(x+8\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-8\right)\left(x+8\right) and \left(x-8\right)\left(-x-8\right) is \left(x-8\right)\left(x+8\right). Multiply \frac{6-x}{\left(x-8\right)\left(-x-8\right)} times \frac{-1}{-1}.
\frac{x-2-\left(-\left(6-x\right)\right)}{\left(x-8\right)\left(x+8\right)}
Since \frac{x-2}{\left(x-8\right)\left(x+8\right)} and \frac{-\left(6-x\right)}{\left(x-8\right)\left(x+8\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x-2+6-x}{\left(x-8\right)\left(x+8\right)}
Do the multiplications in x-2-\left(-\left(6-x\right)\right).
\frac{4}{\left(x-8\right)\left(x+8\right)}
Combine like terms in x-2+6-x.
\frac{4}{x^{2}-64}
Expand \left(x-8\right)\left(x+8\right).
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Limits
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