Algebra trick clarification question I have the equation $x = \sqrt{3} + \sqrt{2} \,\,$ and the trick is that $\frac{1}{x} = \sqrt{3} - \sqrt{2}$. I don't see how the minus sign appears just by taking 1 over x?

\begin{align}
\frac1x &= \frac1{\sqrt{3}+\sqrt{2}}\\
&= \left(\frac1{\sqrt3 + \sqrt2} \right) \left( \frac{\sqrt{3}-\sqrt{2}}{\sqrt3-\sqrt2}\right)\\
&= \frac{\sqrt3-\sqrt2}{3-2}
\end{align}
In general if $x = \sqrt{a}+\sqrt{b} \ne 0, a \ne b$, then $\frac1x = \frac{\sqrt{a}-\sqrt{b}}{a-b}$
