Question

find the domain of ln((x^2-9)/x)

Answer 1

first \[x \neq0\]
and
(x^2-9)/x > 0

Answer 2

think about the natural log, ln(x)=y is asking what power you have to raise e (2.71) to to make it equal to y. Is there any power you can raise e to to get a negative answer (short answer no, but think about why). You also have an x in the denominator there, it can never be zero, the operation of division doesnt make sense when you divide by zero. Dividing by zero is like asking whether the color red is even or odd.