Does anyone know straightforward steps to make the following simplification:
I've tried to make the step:
and multiplying out etc, with the aim of the simplified expression as a factor in the nominator, but then just get into a mess. I'd really like to understand how to spot when such a simplification would be possible.
Thanks for your post. So I can do it now following your suggestion, however it seems very hard to see it without knowing the goal:
LHS of nominator is then straightforward:
but the RHS presents some difficulty without the hindsight of the answer. Grouping the terms (with explicit surd factors) makes the factorisation clear:
Now of course the denominator cancels and you're left with:
Any tips for seeing this pattern in advance?