The least common denominator is $\displaystyle{3}{x}\cdot{7}{y}={21}{x}{y}\usepackage{cmbright}\Huge\$ .

$\displaystyle\frac{{1}}{{{3}{x}}}+\frac{{5}}{{{7}{y}}}=\frac{{1}}{{{3}{x}}}\cdot\frac{{{7}{y}}}{{{7}{y}}}+\frac{{5}}{{{7}{y}}}\cdot\frac{{{3}{x}}}{{{3}{x}}}=\frac{{{7}{y}}}{{{21}{x}{y}}}+\frac{{{15}{x}}}{{{21}{x}{y}}}=\frac{{{7}{y}+{15}{x}}}{{{21}{x}{y}}}\usepackage{cmbright}\Huge\$