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The sum of a number and its reciprocal is $\frac{13}{6}$. Find the number.
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Let the number be $x$. $x + \frac{1}{x} = \frac{13}{6} \Rightarrow 6x^2 - 13x + 6 = 0 \Rightarrow (2x-3)(3x-2) = 0 \Rightarrow x = \frac{3}{2}$ or $\frac{2}{3}$