Question

Rationalize the expression. Write it in simplest form. 9x/√-2x-11

Answer 1

This appears to be just an expression we are simplifying, not an equation we are solving.  I THINK you are saying that the expression looks like this:
$\frac{9x}{ \sqrt{-2x-11} }$
If you rationalize the denominator, you would get this expression:
$\frac{9x}{ \sqrt{-2x-11} } * \frac{ \sqrt{-2x-11} }{ \sqrt{-2x-11} }$
which, after simplifying, looks like this:
$\frac{9x \sqrt{-2x-11} }{-2x-11}$
and that's as simple as I can see that one getting.  You can't factor anything out of the denominator to cancel with the numerator, so I think you're as simple as you can get there!