You may have added the numerators and added the denominators. To add these fractions, rewrite each with the least common denominator, which is $\displaystyle{\left({x}-{2}\right)}{\left({x}+{3}\right)}\usepackage{cmbright}\Huge\$ . Start with:

$\displaystyle\frac{{{7}{x}}}{{{x}-{2}}}+\frac{{4}}{{{x}+{3}}}=\frac{{{\left({7}{x}\right)}{\left({x}+{3}\right)}}}{{{\left({x}-{2}\right)}{\left({x}+{3}\right)}}}+\frac{{{4}{\left({x}-{2}\right)}}}{{{\left({x}+{3}\right)}{\left({x}-{2}\right)}}}\usepackage{cmbright}\Huge\$

Multiply, and then add the numerators. The correct answer is: $\displaystyle\frac{{{7}{{x}}^{{2}}+{25}{x}-{8}}}{{{{x}}^{{2}}+{x}-{6}}}\usepackage{cmbright}\Huge\$