Evaluate
-\frac{x+8}{x^{2}-25}
Expand
-\frac{x+8}{x^{2}-25}
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\frac{2x+7}{\left(x-5\right)\left(x+5\right)}-\frac{3}{x-5}
Factor x^{2}-25.
\frac{2x+7}{\left(x-5\right)\left(x+5\right)}-\frac{3\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and x-5 is \left(x-5\right)\left(x+5\right). Multiply \frac{3}{x-5} times \frac{x+5}{x+5}.
\frac{2x+7-3\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}
Since \frac{2x+7}{\left(x-5\right)\left(x+5\right)} and \frac{3\left(x+5\right)}{\left(x-5\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x+7-3x-15}{\left(x-5\right)\left(x+5\right)}
Do the multiplications in 2x+7-3\left(x+5\right).
\frac{-x-8}{\left(x-5\right)\left(x+5\right)}
Combine like terms in 2x+7-3x-15.
\frac{-x-8}{x^{2}-25}
Expand \left(x-5\right)\left(x+5\right).
\frac{2x+7}{\left(x-5\right)\left(x+5\right)}-\frac{3}{x-5}
Factor x^{2}-25.
\frac{2x+7}{\left(x-5\right)\left(x+5\right)}-\frac{3\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and x-5 is \left(x-5\right)\left(x+5\right). Multiply \frac{3}{x-5} times \frac{x+5}{x+5}.
\frac{2x+7-3\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}
Since \frac{2x+7}{\left(x-5\right)\left(x+5\right)} and \frac{3\left(x+5\right)}{\left(x-5\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x+7-3x-15}{\left(x-5\right)\left(x+5\right)}
Do the multiplications in 2x+7-3\left(x+5\right).
\frac{-x-8}{\left(x-5\right)\left(x+5\right)}
Combine like terms in 2x+7-3x-15.
\frac{-x-8}{x^{2}-25}
Expand \left(x-5\right)\left(x+5\right).
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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