Hello, and welcome !
Your working is perfect until the red message, there is the final step missing.I'm trying to rearrange: √18/(√6+√3) to √6(√2-1).
So I got √18/[√3(√2+1)] which I cancelled down to √6/(√2+1) |||useless ||| and then rearranged to √6(√2+1)^-1. Can anyone please tell me what the next step is? Or have I made a mistake already? Thanks.
Remember the identity .
When you want to "simplify" a denominator containing square roots, this can be very useful because squares of square roots are (in general..) integers!
So here, try to multiply above and below (so that it's fair !) by