What are the critical points for the inequality x^2-9x/x-5

The critical points of an inequality are those points for which the numerator of the denominator equal 0.

First, you need to have an inequality and you have not writen an inequality, so I am going to do an example with an actual inequality bases of some expressions similar to those of the question:

If the ineqquality is (x^2 - 9x ) / (x  - 5) > 0

The critical points are where x^ - 9x = 0 and where x - 5 = 0

1) x^2 - 9x = 0 => x (x - 9) = 0 => x = 0 and x = 9

2) x - 5 = 0 => x = 5

So, for this case the critical points would be 0, 5 and 9.