$\displaystyle\frac{{{{x}}^{{2}}+{7}{x}+{12}}}{{{{x}}^{{2}}+{9}{x}+{20}}}=\frac{{{\left({x}+{3}\right)}{\left({x}+{4}\right)}}}{{{\left({x}+{5}\right)}{\left({x}+{4}\right)}}}\usepackage{cmbright}\Huge\$ , so the domain of the expression excludes both $\displaystyle{x}=-{5}\usepackage{cmbright}\Huge\$ and $\displaystyle{x}=-{4}\usepackage{cmbright}\Huge\$ . Simplifying the expression, you find that $\displaystyle\frac{{{\left({x}+{3}\right)}{\left({x}+{4}\right)}}}{{{\left({x}+{5}\right)}{\left({x}+{4}\right)}}}=\frac{{{x}+{3}}}{{{x}+{5}}}\usepackage{cmbright}\Huge\$ .