Final answer:
To perform the indicated operation, we need to find a common denominator for the two fractions and simplify the numerator.
Step-by-step explanation:
To perform the indicated operation, (2)/(t²-9)-(1)/(t²-2t-3), we need to find a common denominator for the two fractions. The common denominator is (t²-9)(t²-2t-3).
Using this common denominator, we can rewrite the expression as ((2)(t²-2t-3)-(1)(t²-9))/((t²-9)(t²-2t-3)).
Expanding and simplifying the numerator, we get (2t²-4t-6-t²+9) = (t²-4t+3).
So our final answer is (t²-4t+3)/((t²-9)(t²-2t-3)).