#### Answer

$\frac{9n-14}{18}$

#### Work Step by Step

By inspection, we see that the LCM of the denominators is $18$. Therefore, we create a common denominator using this LCM and obtain:
$\frac{4n-3}{6}-\frac{3n+5}{18}$
=$\frac{3(4n-3)-1(3n+5)}{18}$
=$\frac{12n-9-3n-5}{18}$
=$\frac{12n-3n-9-5}{18}$
=$\frac{9n-14}{18}$