Express (√5+4)/(√5-2) in the form p+q√5 where p and q are integers.

Rationalise the denominator by multiplying the whole fraction by (√5+2)/(√5+2). This is equal to one and this removes the surd from the denominator of the fraction, allowing us to solve it.

This gives us
which is equal to

Which gives us 9+5√5.

So p=9 and q=5

Fern H. A Level Maths tutor, GCSE Maths tutor

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