16. $$ \frac{2 t}{2 t^{2}-t-3}-\frac{3}{2 t^{2}-t-3} $$

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To simplify the expression:

$$
\frac{2t}{2t^{2} - t - 3} - \frac{3}{2t^{2} - t - 3}
$$

**Step 1: Combine the Fractions**

Both terms have the same denominator, so you can combine them:

$$
\frac{2t - 3}{2t^{2} - t - 3}
$$

**Step 2: Factor the Denominator**

Factor the quadratic in the denominator:

$$
2t^{2} - t - 3
$$

Look for two numbers that multiply to $$2 \times (-3) = -6$$ and add up to $$-1$$. These numbers are $$-3$$ and $$2$$.

Rewrite the quadratic:

$$
2t^{2} - 3t + 2t - 3 = t(2t - 3) + 1(2t - 3) = (t + 1)(2t - 3)
$$

So, the expression becomes:

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

**Step 3: Simplify by Canceling Common Factors**

Notice that $$2t - 3$$ appears in both the numerator and the denominator. Assuming $$2t - 3 \neq 0$$ (i.e., $$t \neq \frac{3}{2}$$), you can cancel this term:

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

**Final Simplified Form:**

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

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