It appears that you attempted to rewrite the fractions with the same denominator, but multiplied the numerators by the wrong factors. Start with:

$\displaystyle\frac{{5}}{{{2}{x}}}+\frac{{4}}{{{3}{y}}}=\frac{{5}}{{{2}{x}}}\cdot\frac{{{3}{y}}}{{{3}{y}}}+\frac{{4}}{{{3}{y}}}\cdot\frac{{{2}{x}}}{{{2}{x}}}\usepackage{cmbright}\Huge\$

Multiply, and then add the numerators.