let x#y=(x^2)/y for all values of x and y where y does not equal 0. Find all values of x such that x#3=9. Thanks so much!

So a function (?) question.  Also, it doesn't specify whether it should be an integer or not.  I'm guessing you mean an integer.  

We are told that \(x = x\) and \(y=3\).  Plug it in.

\(x\)#\(3\)\(=\dfrac{x^2}{3}\)

Also, \(x\)#\(3=9\).  Plug that in too.

\(9= \dfrac{x^2}{3}\) .  Now multiply both sides by 3 to get rid of the fraction...

\(27=x^2\).  So \(x = \sqrt{27}\).  It is also equal to \(- \sqrt{27}\).  THAT DOES NOT LOOK LIKE A NICE NUMBER.  

Unless I made a mistake which is 100% possible.