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\frac{t-4}{t^{2}-16}
Since \frac{t}{t^{2}-16} and \frac{4}{t^{2}-16} have the same denominator, subtract them by subtracting their numerators.
\frac{t-4}{\left(t-4\right)\left(t+4\right)}
Factor the expressions that are not already factored in \frac{t-4}{t^{2}-16}.
\frac{1}{t+4}
Cancel out t-4 in both numerator and denominator.