Question 377909
h(x) = 7x/[x(x^2 - 9)]

The domain will the all the numbers that we can safely replace x with that will not cause division by zero. Understand?  There is no such thing as division by zero.


In the denominator of your fraction, we have two factors.


The factors are x and (x^2 - 9).


We set each factor to zero and solve for x.


The first one is easy.  We get x = 0.


x^2 - 9 = 0


x^2 = 9


We take the square root of both sides.


sqrt[x^2] = sqrt[9]


Whenever we take the square root, there will be TWO answers.  One answer is positive and the other is negative.



sqrt[x^2] = sqrt[9]


x = -3 and 3.


DOMAIN is: ALL REAL NUMBERS except that x CANNOT equal 0, -3 and 3.


Understand?