#### Answer

$\frac{5}{3}$

#### Work Step by Step

To simplify this expression, we first need to find the common denominator (the LCM) of every denominator, which is $12$. Therefore, we obtain:
$\frac{3}{4}+\frac{2}{3}-\frac{1}{6}+\frac{5}{12}$
=$\frac{3(3)+2(4)-1(2)+5(1)}{12}$
=$\frac{9+8-2+5}{12}$
=$\frac{17+3}{12}$
=$\frac{20}{12}$
=$\frac{5}{3}$