You may have just divided the coefficients and the constants. The correct setup for the problem is:

$\displaystyle\frac{{f{{\left({x}\right)}}}}{{g{{\left({x}\right)}}}}=\frac{{{9}{x}+{6}}}{{{3}{x}+{2}}}\usepackage{cmbright}\Huge\$

Factor the numerator and simplify.