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What is the value of $\frac1x + \frac1y$ if $x = \frac23$ and $y = \frac34$? Express your answer as a mixed number.

Jan 1, 2021

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I found the solution:

$\frac{1}{x} + \frac{1}{y} = \frac{1}{2/3} + \frac{1}{3/4} = \frac32 + \frac43 = \frac{9}{6} + \frac{8}{6} = \frac{17}{6}.$

Writing $\frac{17}{6}$ as a mixed number gives $\boxed{2\frac{5}{6}}$.

Jan 1, 2021