jmc

Let's look at the numerator of the big fraction first. To add $\frac{1}{3}$ to $\frac{1}{4}$, we must first find a common denominator. In this case, it's $12$. So $$\frac{1}{3}+\frac{1}{4}=\frac{1\cdot 4}{3\cdot 4}+\frac{1\cdot 3}{4\cdot 3}=\frac{4}{12}+\frac{3}{12}=\frac{4+3}{12}=\frac{7}{12}.$$Similarly, looking at the denominator of the big fraction, we must again find a common denominator. In this case, it's $30$. So we have $$\frac{2}{5}-\frac{1}{6}=\frac{12}{30}-\frac{5}{30}=\frac{7}{30}.$$Now, the remainder of the problem is to find $\frac{\frac{7}{12}}{\frac{7}{30}}$. Remembering that dividing is the same as multiplying by the reciprocal, we get $$\frac{\frac{7}{12}}{\frac{7}{30}}=\frac{7}{12}\times \frac{30}{7}=\frac{30}{12}.$$But $\frac{30}{12}$ can be written as $\frac{6\cdot 5}{6\cdot 2}$, so our answer simplifies to $\boxed{\frac{5}{2}}$.