Question

rationalize the denominator.
\\(\frac{-9 + w}{\sqrt{w}-\sqrt{u}}=)
type an exact answer using radical notation if necessary.
help: to enter the square root of a number use sqrt(). for example, to give \\(\sqrt{7x}\\) as an answer, you would type sqrt(7x). if you mistakenly type sqrt 7x instead, webwork will take this to mean (x\sqrt{7}), not (\sqrt{7x}). that is, you must put parenthesis around everything that you want to take the square root of.
you have 3 attempt(s) remaining before you will receive a new version of this problem.

Explanation:

Step1: Multiply by conjugate

$\frac{-9 + w}{\sqrt{w}-\sqrt{u}}\times\frac{\sqrt{w}+\sqrt{u}}{\sqrt{w}+\sqrt{u}}$

Step2: Expand numerator and denominator

$\frac{(-9 + w)(\sqrt{w}+\sqrt{u})}{w - u}$
$=\frac{-9\sqrt{w}-9\sqrt{u}+w\sqrt{w}+w\sqrt{u}}{w - u}$

Answer:

$\frac{-9\sqrt{w}-9\sqrt{u}+w\sqrt{w}+w\sqrt{u}}{w - u}$