Question 42114
{{{y = (x +4)/(x^2-4x)}}}
or {{{y = (x+4)/(x(x-4))}}}


Division of a number by zero is not defined.
So, for y to be defined the denominator on the right side must not be 0 i.e. x(x - 4) must not be 0.
So neither x nor (x-4) can be zero.
So x can neither be 0 nor be 4.
This means that y is not-defined for x = 0 and x = 4.
So y is defined for all other values of x.
Hence, the domain is ({{{-infinity}}},0), (0,4) and (4,{{{infinity}}}).


For a more detailed discussion and the use of brackets in designation of domains refer to my lesson at


http://www.algebra.com/tutors/FUNCTIONS.lesson?content_action=show_dev