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As follows:  $\frac{x}{y}+\frac{4}{3}+\frac{9}{2}=\frac{x}{y}+\frac{35}{6}\\ \frac{x}{y} \times \frac{4}{3} \times \frac{9}{2}=6\frac{x}{y}\\ \text{from which it follows that }5\frac{x}{y}=\frac{35}{6}\\ \text{or }\frac{x}{y}=\frac{7}{6}$