Elementary Algebra

$\frac{9n-4}{30}$
First, we find the least common multiple of the denominators of the fractions. This, upon inspection, is found to be $30$. Then, we use the least common multiple to create a common denominator, allowing us to subtract the fractions: $\frac{n+2}{3}-\frac{n-1}{5}+\frac{n-6}{6}$ =$\frac{10(n+2)-6(n-1)+5(n-6)}{30}$ =$\frac{10n+20-6n+6+5n-30}{30}$ =$\frac{10n-6n+5n+20+6-30}{30}$ =$\frac{9n-4}{30}$