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