#### Answer

$\frac{41-15x}{18x}$

#### Work Step by Step

First, we find the least common multiple of the denominators of the fractions. This, upon inspection, is found to be $18x$. Then, we use the least common multiple to create a common denominator, allowing us to combine the fractions:
$\frac{3}{2x}-\frac{5}{6}+\frac{7}{9x}$
=$\frac{3(9)-5(3x)+2(7)}{18x}$
=$\frac{27-15x+14}{18x}$
=$\frac{27+14-15x}{18x}$
=$\frac{41-15x}{18x}$