Evaluate
\frac{x^{2}-3x-34}{\left(x+2\right)\left(x+5\right)}
Expand
\frac{x^{2}-3x-34}{\left(x+2\right)\left(x+5\right)}
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\frac{\left(x-6\right)\left(x+5\right)}{\left(x+2\right)\left(x+5\right)}-\frac{2\left(x+2\right)}{\left(x+2\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+2 and x+5 is \left(x+2\right)\left(x+5\right). Multiply \frac{x-6}{x+2} times \frac{x+5}{x+5}. Multiply \frac{2}{x+5} times \frac{x+2}{x+2}.
\frac{\left(x-6\right)\left(x+5\right)-2\left(x+2\right)}{\left(x+2\right)\left(x+5\right)}
Since \frac{\left(x-6\right)\left(x+5\right)}{\left(x+2\right)\left(x+5\right)} and \frac{2\left(x+2\right)}{\left(x+2\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+5x-6x-30-2x-4}{\left(x+2\right)\left(x+5\right)}
Do the multiplications in \left(x-6\right)\left(x+5\right)-2\left(x+2\right).
\frac{x^{2}-3x-34}{\left(x+2\right)\left(x+5\right)}
Combine like terms in x^{2}+5x-6x-30-2x-4.
\frac{x^{2}-3x-34}{x^{2}+7x+10}
Expand \left(x+2\right)\left(x+5\right).
\frac{\left(x-6\right)\left(x+5\right)}{\left(x+2\right)\left(x+5\right)}-\frac{2\left(x+2\right)}{\left(x+2\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+2 and x+5 is \left(x+2\right)\left(x+5\right). Multiply \frac{x-6}{x+2} times \frac{x+5}{x+5}. Multiply \frac{2}{x+5} times \frac{x+2}{x+2}.
\frac{\left(x-6\right)\left(x+5\right)-2\left(x+2\right)}{\left(x+2\right)\left(x+5\right)}
Since \frac{\left(x-6\right)\left(x+5\right)}{\left(x+2\right)\left(x+5\right)} and \frac{2\left(x+2\right)}{\left(x+2\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+5x-6x-30-2x-4}{\left(x+2\right)\left(x+5\right)}
Do the multiplications in \left(x-6\right)\left(x+5\right)-2\left(x+2\right).
\frac{x^{2}-3x-34}{\left(x+2\right)\left(x+5\right)}
Combine like terms in x^{2}+5x-6x-30-2x-4.
\frac{x^{2}-3x-34}{x^{2}+7x+10}
Expand \left(x+2\right)\left(x+5\right).
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