Write the expression \[\frac{4+6a}{5}-\frac{1+3a}{4}\] as a single fraction.
To write this expression as a single fraction, I need to find a common denominator for the two fractions. The least common multiple of 5 and 4 is 20, so I can multiply the first fraction by 4/4 and the second fraction by 5/5 to get equivalent fractions with a denominator of 20. Doing so, I get \[\frac{4+6a}{5}\cdot\frac{4}{4}-\frac{1+3a}{4}\cdot\frac{5}{5}=\frac{16+24a}{20}-\frac{5+15a}{20}\] Now I can subtract the numerators of the two fractions and keep the common denominator of 20. This gives me \[\frac{16+24a}{20}-\frac{5+15a}{20}=\frac{16+24a-5-15a}{20}=\frac{11+9a}{20}\] This is the simplest form of the expression as a single fraction, so I am done. 