# Adding surd fractions

Fractions with surds can be added or subtracted as regular fractions. However, the denominator should be **rationalised** first.

Here is another example.

\begin{align*} \frac{\sqrt{2}}{\Tblue{1+\sqrt{3}}} - \frac{5}{\Tgreen{\sqrt{2}}} &=\frac{\sqrt{2}(\Tblue{1-\sqrt{3}})}{1-3} - \frac{5\Tgreen{\sqrt{2}}}{2} \\ &=\frac{\sqrt{2}(\sqrt{3}-1)}{2} - \frac{5\sqrt{2}}{2} \\ &=\frac{\sqrt{2}(\sqrt{3}-1-5)}{2} \\ &=\frac{\sqrt{2}(\sqrt{3}-6)}{2} \\ &=\frac{\sqrt{6}}{2} -3\sqrt{2} \end{align*}