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If \(\displaystyle \frac{x}{y} + \frac{4}{3} + \frac{9}{2} = \frac{x}{y} \times \frac{4}{3} \times \frac{9}{2}\) for positive integers x and y, find the smallest possible value of x and y.

 May 15, 2020
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As follows:  \(\frac{x}{y}+\frac{4}{3}+\frac{9}{2}=\frac{x}{y}+\frac{35}{6}\\ \frac{x}{y} \times \frac{4}{3} \times \frac{9}{2}=6\frac{x}{y}\\ \text{from which it follows that }5\frac{x}{y}=\frac{35}{6}\\ \text{or }\frac{x}{y}=\frac{7}{6}\)

 May 15, 2020

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