Evaluate
\frac{x^{2}+7x+40}{x^{2}-25}
Expand
\frac{x^{2}+7x+40}{x^{2}-25}
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\frac{\left(x+5\right)\left(x+5\right)}{\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 x-5 and x+5 is \left(x-5\right)\left(x+5\right). Multiply \frac{x+5}{x-5} times \frac{x+5}{x+5}. Multiply \frac{3}{x+5} times \frac{x-5}{x-5}.
\frac{\left(x+5\right)\left(x+5\right)-3\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}
Since \frac{\left(x+5\right)\left(x+5\right)}{\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{x^{2}+5x+5x+25-3x+15}{\left(x-5\right)\left(x+5\right)}
Do the multiplications in \left(x+5\right)\left(x+5\right)-3\left(x-5\right).
\frac{x^{2}+7x+40}{\left(x-5\right)\left(x+5\right)}
Combine like terms in x^{2}+5x+5x+25-3x+15.
\frac{x^{2}+7x+40}{x^{2}-25}
Expand \left(x-5\right)\left(x+5\right).
\frac{\left(x+5\right)\left(x+5\right)}{\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 x-5 and x+5 is \left(x-5\right)\left(x+5\right). Multiply \frac{x+5}{x-5} times \frac{x+5}{x+5}. Multiply \frac{3}{x+5} times \frac{x-5}{x-5}.
\frac{\left(x+5\right)\left(x+5\right)-3\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}
Since \frac{\left(x+5\right)\left(x+5\right)}{\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{x^{2}+5x+5x+25-3x+15}{\left(x-5\right)\left(x+5\right)}
Do the multiplications in \left(x+5\right)\left(x+5\right)-3\left(x-5\right).
\frac{x^{2}+7x+40}{\left(x-5\right)\left(x+5\right)}
Combine like terms in x^{2}+5x+5x+25-3x+15.
\frac{x^{2}+7x+40}{x^{2}-25}
Expand \left(x-5\right)\left(x+5\right).
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