Answer
The equation has one solution, -4.
Work Step by Step
$\frac{3+a}{2a}=\frac{1}{3}+\frac{5}{6a}$
$\frac{3(3+a)}{6a}-\frac{2a}{6a}-\frac{5}{6a}=0$
$\frac{3a+9}{6a}-\frac{2a}{6a}-\frac{5}{6a}=0$
$\frac{3a+9-2a-5}{6a}=0$
$a+4=0\times6a$
$a+4=0$
$a=-4$
Check:
$(3-4)/[2\times(-4)]=-1/-8=1/8;1/3+5/[6\times(-4)]=1/3-5/24=1/8$
The equation has one solution, -4.
