Question 684721
You cannot divide by zero. So y^2 - 5y can't be zero.


If it were, then 


y^2 - 5y = 0


y(y - 5) = 0


y = 0 or y - 5 = 0


y = 0 or y = 5


Those last two values make the denominator zero. So we must kick them out of the domain.


So the domain is the set of all real numbers except y can't be 0 or y can't be 5.


In set-builder notation, the domain is <img src="http://latex.codecogs.com/gif.latex?\large \{y|y\in\mathbb{R},y\neq 0,y\neq 5\}" title="\large \{y|y\in\mathbb{R},y\neq 0,y\neq 5\}" />


In interval notation, the domain is <img src="http://latex.codecogs.com/gif.latex?\large \left(-\infty, 0\right)\cup\left(0, 5\right)\cup\left(5, \infty\right)" title="\large \left(-\infty, 0\right)\cup\left(0, 5\right)\cup\left(5, \infty\right)" />