You may have divided the coefficients of like terms in the numerator and denominator. Instead, start with:

$\displaystyle{\left(\frac{{f}}{{g}}\right)}{\left({x}\right)}=\frac{{f{{\left({x}\right)}}}}{{g{{\left({x}\right)}}}}=\frac{{{6}{{x}}^{{2}}+{5}{x}-{4}}}{{{3}{{x}}^{{2}}-{23}{x}-{36}}}\usepackage{cmbright}\Huge\$

Factor the numerator and denominator. Simplify, using common factors. The correct answer is: $\displaystyle\frac{{{2}{x}-{1}}}{{{x}-{9}}}\usepackage{cmbright}\Huge\$