Note that $\displaystyle{5}\usepackage{cmbright}\Huge\$ and $\displaystyle-{3}\usepackage{cmbright}\Huge\$ are excluded values. Multiply both sides by the common denominator $\displaystyle{\left({x}-{5}\right)}{\left({x}+{3}\right)}\usepackage{cmbright}\Huge\$ :

$\displaystyle\frac{{{12}{\left({x}-{5}\right)}{\left({x}+{3}\right)}}}{{{x}-{5}}}=\frac{{{4}{\left({x}-{5}\right)}{\left({x}+{3}\right)}}}{{{x}+{3}}}\usepackage{cmbright}\Huge\$

Simplify: $\displaystyle{12}{\left({x}+{3}\right)}={4}{\left({x}-{5}\right)}\usepackage{cmbright}\Huge\$

Distribute: $\displaystyle{12}{x}+{36}={4}{x}-{20}\usepackage{cmbright}\Huge\$

Solve for x: $\displaystyle{12}{x}={4}{x}-{56}\usepackage{cmbright}\Huge\$ , $\displaystyle{8}{x}=-{56}\usepackage{cmbright}\Huge\$ , $\displaystyle{x}=-{7}\usepackage{cmbright}\Huge\$