I have seen in the solutions that the first step is to multiply (rt3-6)/rt3 by rt3/rt3 and I can work it through from that point onwards; however, I don't understand why/how we do the first step.

How do we know to multiply by rt3/rt3?

Thanks

The GMAC writers don't like square roots in the denominator.
Multiplying by sqrt3 / sqrt3 won't change the value, since sqrt3 / sqrt3 = 1, but it will turn the denominator into 3 instead of something with a square root in it.

If we have a square root in the denominator, our first step is to try to turn it into something without a root. Usually, this involves multiplying it by itself. If we have sqrt(5) in the denominator, we'd multiply by sqrt5 / sqrt5.
On the other hand, if we had 2*sqrt7 in the denominator, we could multiply by sqrt7/sqrt7 and end up with 14 in the denominator. (It's not necessary to multiply by 2sqrt7/2sqrt7, as the goal is to get rid of the sqrt7...

Hope this answers your question!

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