Answer
$\frac{1}{t+1}$
Work Step by Step
Since we already have common denominators, we can add and simplify the numerators:
$\frac{2t}{2t^2 -t -3} - \frac{3}{2t^2 -t -3} =\frac{2t - 3}{2t^2 -t -3}$
We now need to factor the denominator to see if there are any common factors:
$\frac{2t - 3}{2t^2 -t -3}= \frac{2t - 3}{(2t-3)(t+1)}$; $(2t - 3)$ will cancel from the numerator and denominator: $ \frac{2t - 3}{(2t-3)(t+1)} = \frac{1}{t+1}$
