Math Help - Simplify expression

1. Simplify expression

Howdy I could use a little help solving this problem.
(2*(x+11)^(1/2)-x*(x+11)^(-1/2))/(x+11)

2. Factor out $(x+11)^{-1/2}$ in the numerator, then cancel it out in the denominator.

3. Could you explain how those two factor out the (x+11) on the bottom? If I understand you correctly, the top two should negate out to 1?

4. wait... does it simplify to -9/11 ?

5. Hello, Nyture!

Simplify: . $\frac{2(x+11)^{\frac{1}{2}} -x(x+11)^{-\frac{1}{2}}} {x+11}$
Multiply by $\frac{(x+11)^{\frac{1}{2}}}{(x+11)^{\frac{1}{2}}}$

. . $\frac{(x+11)^{\frac{1}{2}}}{(x+11)^{\frac{1}{2}}} \cdot \frac{2(x+11)^{\frac{1}{2}} - x(x+11)^{-\frac{1}{2}}}{x+11} \;\;=\;\;\frac{2(x+11) - x}{(x+11)^{\frac{3}{2}}}$

. . . . . . . $= \;\;\frac{2x + 22 - x}{(x+11)^{\frac{3}{2}}} \;\;=\;\;\frac{x+22}{(x+11)^{\frac{3}{2}}}$

6. Ugh, I came up with that answer about 5 times but I guess I never plugged it in. Good to know what the actual right answer is so I can stop reworking. Thanks a lot of the help!