my text says that
2 (x-3)^(1/2) - x(x- 3)^(-1/2)
-----------------------------------
x-3
is equal to
(x-3)^(-1/2) [2 (x-3) - x ]
--------------------------------
x- 3
but where did the 1/2 exponent for (x-3) go?
Hi kingsolomonsgrave!
Suppose we only look at the nominator to keep things simple.
And suppose we define $\displaystyle y=(x-3)^{1/2}$.
Then this implies that $\displaystyle y^{-1}=(x-3)^{-1/2}$ (do you know why?).
It also implies that $\displaystyle y^2 = (x-3)$.
If we substitute these into your first nominator, you'll get:
$\displaystyle 2 y - x y^{-1}$
And if we substitute them into your second nominator, you'll get:
$\displaystyle y^{-1} [ 2 y^2 - x ]$
Can you see that those expressions are identical?