Question 1163980
<pre>
You need to review how to handle "reversed differences":

The shortcut is

{{{(A-B)/(B-A)}}}{{{""=""}}}{{{-1}}}

No doubt that is why you got the sign wrong.

Anyway, let's do your problem:

{{{lim["x->9"]((9-x)/(sqrt(x)-3))}}}

{{{lim["x->9"]((9-x)/(sqrt(x)-3))(expr((sqrt(x)+3)/(sqrt(x)+3)))}}}

Multiply the bottoms only:

{{{lim["x->9"](((9-x)(sqrt(x)+3))/(x-9)))}}}

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["x->9"](((-x+9)(sqrt(x)+3))/(x-9)))}}}

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

{{{lim["x->9"](((-1(x-9))(sqrt(x)+3))/(x-9))}}}

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

{{{lim["x->9"](((-1(cross(x-9)))(sqrt(x)+3))/(cross(x-9)))}}}

{{{lim["x->9"](-1)(sqrt(x)+3)}}}

Now you can substitute 9 for x:

{{{(-1)(sqrt(9)+3)}}}

{{{(-1)(3+3)}}}

{{{-6}}}

Edwin</pre>