# Thread: why are these equal?

1. ## why are these equal?

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?

2. ## Re: why are these equal?

Originally Posted by kingsolomonsgrave
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
What does $y^{-1/2}(y-1)=~?$

3. ## Re: why are these equal?

Hi kingsolomonsgrave!

Suppose we only look at the nominator to keep things simple.
And suppose we define $y=(x-3)^{1/2}$.
Then this implies that $y^{-1}=(x-3)^{-1/2}$ (do you know why?).
It also implies that $y^2 = (x-3)$.

If we substitute these into your first nominator, you'll get:
$2 y - x y^{-1}$

And if we substitute them into your second nominator, you'll get:
$y^{-1} [ 2 y^2 - x ]$

Can you see that those expressions are identical?