It appears that you combined the original numerators while changing the denominators to the correct LCD. Instead, rewrite each term as an equivalent fraction before adding or subtracting:

$\displaystyle\frac{{7}}{{{12}{{b}}^{{3}}}}+\frac{{{9}{{a}}^{{2}}}}{{{10}{{b}}^{{5}}}}-\frac{{{4}{a}}}{{{15}{b}}}=\frac{{{7}{\left({5}{{b}}^{{2}}\right)}}}{{{\left({12}{{b}}^{{3}}\right)}{\left({5}{{b}}^{{2}}\right)}}}+\frac{{{9}{{a}}^{{2}}{\left({6}\right)}}}{{{\left({10}{{b}}^{{5}}\right)}{\left({6}\right)}}}-\frac{{{4}{a}{\left({4}{{b}}^{{4}}\right)}}}{{{\left({15}{b}\right)}{\left({4}{{b}}^{{4}}\right)}}}\usepackage{cmbright}\Huge\$

Then simplify and combine the numerators.