$\frac{1}{2} - \frac{1}{3} = \frac{3}{x}$. What is the value of $x$?

$$\boxed{
\small{\text{
~~$\frac{1}{2} - \frac{1}{3} = \frac{3}{x}$. What is the value of $x$~?
}}}\\\\\\
\small{\text{$
\begin{array}{rcl}
\dfrac{1}{2} - \dfrac{1}{3} &=& \dfrac{3}{x}\\\\
\dfrac{1}{2}\cdot\dfrac33 - \dfrac{1}{3}\cdot\dfrac22 &=& \dfrac{3}{x}\\\\
\dfrac{3-2}{6} &=& \dfrac{3}{x}\\\\
\dfrac{1}{6} &=& \dfrac{3}{x}\\\\
\dfrac{6}{1} &=& \dfrac{x}{3}\\\\
6 &=& \dfrac{x}{3}\\\\
\dfrac{x}{3} &=& 6 \quad | \quad \cdot 3\\\\
x &=& 6 \cdot 3\\\\
\mathbf{x} & \mathbf{=} & \mathbf{18}\\\\
\end{array}
$}}$$

 

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