$\displaystyle\frac{{{12}{{x}}^{{2}}+{6}{x}}}{{{6}{{x}}^{{3}}+{6}{x}}}=\frac{{{\left({6}{x}\right)}{\left({2}{x}+{1}\right)}}}{{{\left({6}{x}\right)}{\left({{x}}^{{2}}+{1}\right)}}}\usepackage{cmbright}\Huge\$ , so the domain of the expression excludes $\displaystyle{x}={0}\usepackage{cmbright}\Huge\$ (since when $\displaystyle{x}={0}\usepackage{cmbright}\Huge\$ , $\displaystyle{6}{x}={0}\usepackage{cmbright}\Huge\$ ). Notice that the expression $\displaystyle{{x}}^{{2}}+{1}\usepackage{cmbright}\Huge\$ cannot be 0, so no additional values need to be excluded. Simplifying the expression, you find that $\displaystyle\frac{{{\left({6}{x}\right)}{\left({2}{x}+{1}\right)}}}{{{\left({6}{x}\right)}{\left({{x}}^{{2}}+{1}\right)}}}=\frac{{{2}{x}+{1}}}{{{{x}}^{{2}}+{1}}}\usepackage{cmbright}\Huge\$ .