Solve for $x$: $$ \frac{1}{2} - \frac{1}{3} = \frac{1}{x}.$$
To solve for $x$, I need to isolate it on one side of the equation. I can do this by multiplying both sides by $x$, which gives me $$ x \left( \frac{1}{2} - \frac{1}{3} \right) = 1.$$ Now I need to simplify the expression in parentheses by finding a common denominator. The lowest common denominator of $2$ and $3$ is $6$, so I can rewrite the fractions as $$ x \left( \frac{3}{6} - \frac{2}{6} \right) = 1.$$ Combining the fractions, I get $$ x \left( \frac{1}{6} \right) = 1.$$ To get rid of the fraction, I can multiply both sides by $6$, which gives me $$ x = 6.$$ 