SOLUTION: lim as x approaches 9 (9-x/sqrtx-3) answer to this question is -6 but i got 6 could u explain me the apprach

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Question 1163980: lim as x approaches 9 (9-x/sqrtx-3) answer to this question is -6 but i got 6 could u explain me the apprach
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
You need to review how to handle "reversed differences":

The shortcut is

%28A-B%29%2F%28B-A%29%22%22=%22%22-1

No doubt that is why you got the sign wrong.

Anyway, let's do your problem:

lim%5B%22x-%3E9%22%5D%28%289-x%29%2F%28sqrt%28x%29-3%29%29



Multiply the bottoms only:

lim%5B%22x-%3E9%22%5D%28%28%289-x%29%28sqrt%28x%29%2B3%29%29%2F%28x-9%29%29%29

Have you learned the shortcut trick about reversed differences? 
That is, that (x-9) cancels into (9-x) and goes -1 times?
If you have, fine, then use it.  But if you haven't learned that
trick, then write 9-x in descending order -x+9 then factor out -1 
and get -1(x-9), like this:

Write 9-x in descending order as -x+9

lim%5B%22x-%3E9%22%5D%28%28%28-x%2B9%29%28sqrt%28x%29%2B3%29%29%2F%28x-9%29%29%29

Then factor -1 out of -x+9 which changes the signs:

lim%5B%22x-%3E9%22%5D%28%28%28-1%28x-9%29%29%28sqrt%28x%29%2B3%29%29%2F%28x-9%29%29

Now you can cancel the (x-9)'s



lim%5B%22x-%3E9%22%5D%28-1%29%28sqrt%28x%29%2B3%29

Now you can substitute 9 for x:

%28-1%29%28sqrt%289%29%2B3%29

%28-1%29%283%2B3%29

-6

Edwin