# How do you find the critical numbers of #y = (x^2-4)/(x^2-2x)#?

##### 1 Answer

Mar 23, 2017

First things first, the function can be simplified as follows:

#y = ((x + 2)(x - 2))/(x(x - 2))#

#y = (x+ 2)/x#

#y = x/x + 2/x#

#y = 1 + 2/x#

The derivative of this is

#y' = -2/x^2#

There are critical numbers when the derivative is undefined or the derivative equals

#0 = -2/x^2#

#0 = -2#

This is obviously a contradiction, therefore the equation

Hopefully this helps!