lim when x approaches a (√x - √a) / x-a

I did this:
(√x - √a) / x-a = (x+a) / ( (x-a)(√x - √a) )
= (a+a) / ( (a-a)(√a - √a) ) = 2a/0 = Does not exist

But I'm not sure I did that right.

Question

lim when x approaches a (√x - √a) / x-a

I did this: 
(√x - √a) / x-a = (x+a) / ( (x-a)(√x - √a) )
= (a+a) / ( (a-a)(√a - √a) ) = 2a/0 = Does not exist

But I'm not sure I did that right.

myininaya · Answer

instead factor the denominator.

myininaya · Answer

$$x-a=(\sqrt{x}-\sqrt{a})(\sqrt{x}+\sqrt{a})$$

myininaya · Answer

I just treated it like it was a difference of squares basically

myininaya · Answer

if you don't like that way. Relation the numerator. You sorta did it incorrectly above.

darkigloo · Answer

i did the way you said an i got 2√a

myininaya · Answer

one over that right?

darkigloo · Answer

oh yeah.