What is rationalising a fraction?

So firstly, when we do a rationalisation problem, we are trying to get rid of any surds in the denominator(the bottom part of a fraction). Surds are numbers that have been square rooted and do not equal a whole number, and can be identified by any number with a √ sign before it. Normally, a question like this looks like this: Rationalise this expression (3 - √7)/(5 + √7). Remember to rationalise, we only need to get rid of the surd in the denominator! We do this by multiplying both the top half of the fraction and the bottom half of the fraction by (5 - √7). What do you notice about this?We can see that anything divided by itself is 1, so all we're doing is multiplying the original expression by 1. Also the expression we are timesing both halves by is the same as the denominator but we have changed the sign in the middle. This is crucial as it will allow for us to 'cancel' out the surd. We then carry out the multiplication: (3-√7)(5-√7)/(5+√7)(5-√7) = (15 - 3√7 - 5√7 + (√7)^2)/ 25 - 5√7 +5√7 - (√7)^2. As the surd is a square root, squaring it means it equals the number within the √ sign. So (√7)^2 = 7. Also, 5√7 - 5√7 = 0 so in the denominator we are left with 25 - 7 =18. Overall we are left with:(22-8√7)/18. We have successfully rationalised the denominator as there is no surd left in the bottom! Now you try:Rationalise this expression: (9+√2)/(4 - √3)