How do I solve operations involving fractional surds? [duplicate]

In general, for a fraction that resembles $\frac{a}{\sqrt{b} + \sqrt{c}}$, you could multiply it by $\frac{\sqrt{b} - \sqrt{c}}{\sqrt{b} - \sqrt{c}}$ (which is equal to $1$) to cause the denominator to become a rational number. For this reason, this process is known as "rationalizing" the expression.

So for example, $$\begin{align}\frac{\sqrt{2} + \sqrt{3}}{\sqrt{7} - \sqrt{5}} &= \frac{\sqrt{2} + \sqrt{3}}{\sqrt{7} - \sqrt{5}}\cdot\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}\\ &= \frac{\sqrt{14} + \sqrt{21} + \sqrt{10} + \sqrt{15}}{7 - 5}\\ &= \frac{1}{2}\cdot(\sqrt{14} + \sqrt{21} + \sqrt{10} + \sqrt{15})\end{align}$$

For your questions, you might try combining each of them into a single fraction. Some of them automatically gets rationalized (e.g. (a) and (b)). Otherwise if the denominator of the result is not a rational number, you can then go ahead to "rationalize" the resultant expression as described above.