Can you teach me how to rationalise the denominator of an algebraic expression?

You may be asked to rationalise the denominator of an algebraic expression if it contains a surd in the denominator - such as a^1/2. They can get slightly more complex than this though! What it is asking for when the question asks you to rationalise the denominator is to remove the surd from the denominator of the algebraic expression.
We want to multiply the numerator and denominator of the algebraic expression by the denominator itself (so a^1/2 ). The reason we do this is that this multiplying a surd by itself results in the surd disappearing (e.g. a^1/2 * a^1/2 = a ), therefore removing the surd that we do not want in the denominator. So the denominator will now not contain a surd (just as the question asks!). The numerator will result in being the product of the original numerator and the original denominator. It is okay to have a surd in the numerator, the question asks only to remove the surds from the denominator.