How do I simplify a fraction with surds on the bottom when the surd is part of a function?

When doing questions like this you simply times the top and bottom of the fraction by the bottom function but with a sign change. For example if "5 - √3" was the denominator of the fraction (on the bottom of the fraction) you would times the top and bottom of the fraction by "5 + √3". Note that it is only the sign in front of the surd that changes.

Here is a worked example of an exam question:

(4 + 2√2) / (2 - √2)

(4 + 2√2)(2 + √2) / (2 - √2)(2 + √2)

Use FOIL to expand the brackets: (8 + 4√2 + 4√2 + 4) / (4 + 2√2 - 2√2 -2)

SIMPLIFY

(12 + 8√2) / 2 = 6 + 4√2