Answer
$\frac{2}{t-3}$
Work Step by Step
$\frac{2t+6}{t^{2}-9}=\frac{2(t+3)}{(t+3)(t-3)}=\frac{2}{t-3}\times\frac{t+3}{t+3}=\frac{2}{t-3}\times1=\frac{2}{t-3}$
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