problem: Write the expression \[\frac{4+6a}{5}-\frac{1+3a}{4}\] as a single fraction.
solution: The common denominator of $5$ and $4$ is $20$, so we multiply top and bottom of the first fraction by $4$ and multiply top and bottom of the second fraction by $5$. We get \[\frac{4(4+6a)}{4 \cdot 5} - \frac{5(1+3a)}{4 \cdot 5} = \frac{16+24a}{20}-\frac{5+15a}{20}.\] We combine the fractions, being careful to put the numerator of the second fraction in parentheses (as we are subtracting the entire numerator), yielding \[\frac{16+24a-(5+15a)}{20} = \frac{16+24a-5-15a}{20}=\boxed{\frac{11+9a}{20}}.\]