The least common denominator is $\displaystyle{5}{x}\cdot{3}{y}={15}{x}{y}\usepackage{cmbright}\Huge\$ .

$\displaystyle\frac{{4}}{{{5}{x}}}+\frac{{7}}{{{3}{y}}}=\frac{{4}}{{{5}{x}}}\cdot\frac{{{3}{y}}}{{{3}{y}}}+\frac{{7}}{{{3}{y}}}\cdot\frac{{{5}{x}}}{{{5}{x}}}=\frac{{{12}{y}}}{{{15}{x}{y}}}+\frac{{{35}{x}}}{{{15}{x}{y}}}=\frac{{{12}{y}+{35}{x}}}{{{15}{x}{y}}}\usepackage{cmbright}\Huge\$