So anyone have any idea on how to solve this one? I've tried all the usual ways to solve..getting no where fast.
Hello,
The conjugate of a number a-b is a+b (and conversely). (a-b)(a+b)=aČ-bČ. This is why it can be very useful when you want to get rid of some square roots, or transforming a difference into a sum.
Multiply by $\displaystyle 1=\frac{\sqrt{3-x}+1}{\sqrt{3-x}+1}$
Small mistake:
Multiply by $\displaystyle 1=\frac{\sqrt{3-x}{\color{red}+}1}{\sqrt{3-x}{\color{red}+}1}$
To the OP: I'm very surprised that what moo showed you wasn't on your check list of all the usual ways ..... Clearly moo made a typo that you should have realised and corrected for.
Yeah it was a typo on my part. I've done the conjugate thing a few times on this problem and keep getting stuck trying to get an x-2 factored from the top.
I get stuck even after I foil the numerator I end up with:
$\displaystyle
\frac{(\sqrt{6-x})(\sqrt{3-x})-2(\sqrt{3-x}+\sqrt{6-x}-2}{2-x}
$