Evaluate
\frac{3z^{2}-15z-4}{z^{2}-16}
Expand
\frac{3z^{2}-15z-4}{z^{2}-16}
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\frac{\left(3z-1\right)\left(z-4\right)}{\left(z-4\right)\left(z+4\right)}-\frac{2\left(z+4\right)}{\left(z-4\right)\left(z+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z+4 and z-4 is \left(z-4\right)\left(z+4\right). Multiply \frac{3z-1}{z+4} times \frac{z-4}{z-4}. Multiply \frac{2}{z-4} times \frac{z+4}{z+4}.
\frac{\left(3z-1\right)\left(z-4\right)-2\left(z+4\right)}{\left(z-4\right)\left(z+4\right)}
Since \frac{\left(3z-1\right)\left(z-4\right)}{\left(z-4\right)\left(z+4\right)} and \frac{2\left(z+4\right)}{\left(z-4\right)\left(z+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3z^{2}-12z-z+4-2z-8}{\left(z-4\right)\left(z+4\right)}
Do the multiplications in \left(3z-1\right)\left(z-4\right)-2\left(z+4\right).
\frac{3z^{2}-15z-4}{\left(z-4\right)\left(z+4\right)}
Combine like terms in 3z^{2}-12z-z+4-2z-8.
\frac{3z^{2}-15z-4}{z^{2}-16}
Expand \left(z-4\right)\left(z+4\right).
\frac{\left(3z-1\right)\left(z-4\right)}{\left(z-4\right)\left(z+4\right)}-\frac{2\left(z+4\right)}{\left(z-4\right)\left(z+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z+4 and z-4 is \left(z-4\right)\left(z+4\right). Multiply \frac{3z-1}{z+4} times \frac{z-4}{z-4}. Multiply \frac{2}{z-4} times \frac{z+4}{z+4}.
\frac{\left(3z-1\right)\left(z-4\right)-2\left(z+4\right)}{\left(z-4\right)\left(z+4\right)}
Since \frac{\left(3z-1\right)\left(z-4\right)}{\left(z-4\right)\left(z+4\right)} and \frac{2\left(z+4\right)}{\left(z-4\right)\left(z+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3z^{2}-12z-z+4-2z-8}{\left(z-4\right)\left(z+4\right)}
Do the multiplications in \left(3z-1\right)\left(z-4\right)-2\left(z+4\right).
\frac{3z^{2}-15z-4}{\left(z-4\right)\left(z+4\right)}
Combine like terms in 3z^{2}-12z-z+4-2z-8.
\frac{3z^{2}-15z-4}{z^{2}-16}
Expand \left(z-4\right)\left(z+4\right).
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