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 + 22) / (2 - 2)

(4 + 22)(2 + 2) / (2 - 2)(2 + 2)

Use FOIL to expand the brackets: (8 + 42 + 42 + 4) / (4 + 22 - 22 -2)

SIMPLIFY

(12 + 82) / 2 = 6 + 42

Answered by Charlotte W. Maths tutor

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