Evaluate
\frac{x+5}{x^{2}-36}
Expand
\frac{x+5}{x^{2}-36}
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\frac{x^{2}-25}{\left(x-6\right)\left(x+6\right)}-\frac{x+5}{x+6}
Factor x^{2}-36.
\frac{x^{2}-25}{\left(x-6\right)\left(x+6\right)}-\frac{\left(x+5\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-6\right)\left(x+6\right) and x+6 is \left(x-6\right)\left(x+6\right). Multiply \frac{x+5}{x+6} times \frac{x-6}{x-6}.
\frac{x^{2}-25-\left(x+5\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)}
Since \frac{x^{2}-25}{\left(x-6\right)\left(x+6\right)} and \frac{\left(x+5\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-25-x^{2}+6x-5x+30}{\left(x-6\right)\left(x+6\right)}
Do the multiplications in x^{2}-25-\left(x+5\right)\left(x-6\right).
\frac{5+x}{\left(x-6\right)\left(x+6\right)}
Combine like terms in x^{2}-25-x^{2}+6x-5x+30.
\frac{5+x}{x^{2}-36}
Expand \left(x-6\right)\left(x+6\right).
\frac{x^{2}-25}{\left(x-6\right)\left(x+6\right)}-\frac{x+5}{x+6}
Factor x^{2}-36.
\frac{x^{2}-25}{\left(x-6\right)\left(x+6\right)}-\frac{\left(x+5\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-6\right)\left(x+6\right) and x+6 is \left(x-6\right)\left(x+6\right). Multiply \frac{x+5}{x+6} times \frac{x-6}{x-6}.
\frac{x^{2}-25-\left(x+5\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)}
Since \frac{x^{2}-25}{\left(x-6\right)\left(x+6\right)} and \frac{\left(x+5\right)\left(x-6\right)}{\left(x-6\right)\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-25-x^{2}+6x-5x+30}{\left(x-6\right)\left(x+6\right)}
Do the multiplications in x^{2}-25-\left(x+5\right)\left(x-6\right).
\frac{5+x}{\left(x-6\right)\left(x+6\right)}
Combine like terms in x^{2}-25-x^{2}+6x-5x+30.
\frac{5+x}{x^{2}-36}
Expand \left(x-6\right)\left(x+6\right).
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