# Chapter 11 - Rational Expressions and Functions - 11-4 Adding and Subtracting Rational Expressions - Practice and Problem-Solving Exercises - Page 675: 16

$\frac{1}{t+1}$

#### 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: $\frac{2t - 3}{(2t-3)(t+1)} = \frac{1}{t+1}$

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