$\displaystyle{9}{{m}}^{{2}}{n}={3}\cdot{3}\cdot{m}\cdot{m}\cdot{n}\usepackage{cmbright}\Huge\$ and $\displaystyle{12}{n}={2}\cdot{2}\cdot{3}\cdot{n}\usepackage{cmbright}\Huge\$ , so the LCM $\displaystyle={2}\cdot{2}\cdot{3}\cdot{3}\cdot{m}\cdot{m}\cdot{n}={36}{{m}}^{{2}}{n}\usepackage{cmbright}\Huge\$

$\displaystyle\frac{{{m}+{2}}}{{{9}{{m}}^{{2}}{n}}}+\frac{{5}}{{{12}{n}}}=\frac{{{\left({m}+{2}\right)}{\left({4}\right)}}}{{{\left({9}{{m}}^{{2}}{n}\right)}{\left({4}\right)}}}+\frac{{{5}{\left({3}{{m}}^{{2}}\right)}}}{{{12}{n}{\left({3}{{m}}^{{2}}\right)}}}=\frac{{{4}{m}+{8}}}{{{36}{{m}}^{{2}}{n}}}+\frac{{{15}{{m}}^{{2}}}}{{{36}{{m}}^{{2}}{n}}}\usepackage{cmbright}\Huge\$

$\displaystyle=\frac{{{15}{{m}}^{{2}}+{4}{m}+{8}}}{{{36}{{m}}^{{2}}{n}}}\usepackage{cmbright}\Huge\$