SOLUTION: find the domain x^5-7x/x^3-2

Question 822561: find the domain
x^5-7x/x^3-2
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Please use parentheses around numerators and denominators, especially if they are more than just a positive integer or variable. What you posted, without parentheses meant:

Since the fraction reduces easily I doubt this is what you intended. I suspect it should be
or
which should be posted as:
(x^5-7x)/(x^3-2) or x^5-7x/(x^3-2)
Tutors are more likely to respond if the problem is clearly posted.

To find the domain of or we use the fact that numerators can be any number but denominators can be any number except zero!. So the numerator has nothing to do with the domain. The domain will be any real number except any numbers which would make the denominator.

Since the two possible expressions have the same denominator, they will have the same domain. To find the numbers, if any, which make the denominator zero we set the denominator to zero:

and solve. Adding 2:

Cube root of each side:

This is the only number that makes the denominator zero. So it is the only number which is not in the domain. The domain is all real numbers except .
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