Answer
$\frac{1}{(\sqrt{t+3}+\sqrt 3)}$
Work Step by Step
$\frac{\sqrt{t+3}-\sqrt 3}{t}=\frac{(\sqrt{t+3}-\sqrt 3)(\sqrt{t+3}+\sqrt 3)}{t(\sqrt{t+3}+\sqrt 3)}=\frac{t+3-3}{t(\sqrt{t+3}+\sqrt 3)}=\frac{t}{t(\sqrt{t+3}+\sqrt 3)}=\frac{1}{(\sqrt{t+3}+\sqrt 3)}$