$\displaystyle\frac{{{5}{{x}}^{{3}}+{15}{{x}}^{{2}}+{10}{x}}}{{{3}{{x}}^{{3}}-{3}{x}}}=\frac{{{5}{x}{\left({x}+{2}\right)}{\left({x}+{1}\right)}}}{{{3}{x}{\left({x}-{1}\right)}{\left({x}+{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{3}{x}={0}\usepackage{cmbright}\Huge\$ ), 1, and -1. Simplifying the expression, you find that $\displaystyle\frac{{{5}{{x}}^{{3}}+{15}{{x}}^{{2}}+{10}{x}}}{{{3}{{x}}^{{3}}-{3}{x}}}=\frac{{{5}{\left({x}+{2}\right)}}}{{{3}{\left({x}-{1}\right)}}}\usepackage{cmbright}\Huge\$ .