$3-frac{3+sqrt{5}}{4}-frac{1}{3+sqrt{5}}$ is equal to

$frac{1}{3+sqrt{5}}=frac{3-sqrt{5}}{(3+sqrt{5})(3-sqrt{5})}$

$=frac{3-sqrt{5}}{9-5}=frac{3-sqrt{5}}{4}$

$3-frac{3+sqrt{5}}{4}-frac{3-sqrt{5}}{4}$

$=frac{12-3-sqrt{5}-3+sqrt{5}}{4}=frac{6}{4}=frac{3}{2}$