To simplify the expression \( 3/(2 + \sqrt{t}) \), you can rationalize the denominator. To do this, you'll multiply both the numerator and the denominator by the conjugate of the denominator, which is \( 2 - \sqrt{t} \):
\[ \frac{3}{2 + \sqrt{t}} \cdot \frac{2 - \sqrt{t}}{2 - \sqrt{t}} = \frac{3(2 - \sqrt{t})}{(2 + \sqrt{t})(2 - \sqrt{t})} \]
Now, we simplify the denominator:
\[ (2 + \sqrt{t})(2 - \sqrt{t}) = 2^2 - (\sqrt{t})^2 = 4 - t \]
Now substitute this back into the expression:
\[ \frac{3(2 - \sqrt{t})}{4 - t} \]
Thus, the simplified expression is:
\[ \frac{3(2 - \sqrt{t})}{4 - t} \]