I'm stuck on what should be quite a simple part of householder transforms. I can do them fine except when there's a square root in the middle of it.
For example... suppose I have to transform

so I know I'll be using this:

and know I want to get to H =

But I get stuck on the simple act of multiplying through the -3-(10)^1/2 bits... I end up with the 2w3w3t fraction bit looking like this:

And there's no way I - !that! is going to come out like it should. What I've done is tried to expand it as if it was a quadratic, in order to preserve the square root and not end up with unusable fractions:

But I'm all confused from there!! (Oops, should have a 6 in the one above, not a 3.)
Could anyone join the dots for me please?