Evaluate
\frac{5x^{2}+15x+18}{\left(5x+1\right)\left(x^{2}-16\right)}
Expand
\frac{5x^{2}+15x+18}{\left(5x+1\right)\left(x^{2}-16\right)}
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\frac{x+2}{\left(x-4\right)\left(x+4\right)}+\frac{4}{\left(x-4\right)\left(5x+1\right)}
Factor x^{2}-16. Factor 5x^{2}-19x-4.
\frac{\left(x+2\right)\left(5x+1\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}+\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-4\right)\left(x+4\right) and \left(x-4\right)\left(5x+1\right) is \left(x-4\right)\left(x+4\right)\left(5x+1\right). Multiply \frac{x+2}{\left(x-4\right)\left(x+4\right)} times \frac{5x+1}{5x+1}. Multiply \frac{4}{\left(x-4\right)\left(5x+1\right)} times \frac{x+4}{x+4}.
\frac{\left(x+2\right)\left(5x+1\right)+4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}
Since \frac{\left(x+2\right)\left(5x+1\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)} and \frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)} have the same denominator, add them by adding their numerators.
\frac{5x^{2}+x+10x+2+4x+16}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}
Do the multiplications in \left(x+2\right)\left(5x+1\right)+4\left(x+4\right).
\frac{5x^{2}+15x+18}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}
Combine like terms in 5x^{2}+x+10x+2+4x+16.
\frac{5x^{2}+15x+18}{5x^{3}+x^{2}-80x-16}
Expand \left(x-4\right)\left(x+4\right)\left(5x+1\right).
\frac{x+2}{\left(x-4\right)\left(x+4\right)}+\frac{4}{\left(x-4\right)\left(5x+1\right)}
Factor x^{2}-16. Factor 5x^{2}-19x-4.
\frac{\left(x+2\right)\left(5x+1\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}+\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-4\right)\left(x+4\right) and \left(x-4\right)\left(5x+1\right) is \left(x-4\right)\left(x+4\right)\left(5x+1\right). Multiply \frac{x+2}{\left(x-4\right)\left(x+4\right)} times \frac{5x+1}{5x+1}. Multiply \frac{4}{\left(x-4\right)\left(5x+1\right)} times \frac{x+4}{x+4}.
\frac{\left(x+2\right)\left(5x+1\right)+4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}
Since \frac{\left(x+2\right)\left(5x+1\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)} and \frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)} have the same denominator, add them by adding their numerators.
\frac{5x^{2}+x+10x+2+4x+16}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}
Do the multiplications in \left(x+2\right)\left(5x+1\right)+4\left(x+4\right).
\frac{5x^{2}+15x+18}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}
Combine like terms in 5x^{2}+x+10x+2+4x+16.
\frac{5x^{2}+15x+18}{5x^{3}+x^{2}-80x-16}
Expand \left(x-4\right)\left(x+4\right)\left(5x+1\right).
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