SOLUTION: What is the domain and what are the zero(s) of the this function : (9x^(3)-4x)/((x-3)(x^(2)-2x+1)) I have tried long division, simplifying it, and rearranging the equation. I ca

Algebra ->  Functions -> SOLUTION: What is the domain and what are the zero(s) of the this function : (9x^(3)-4x)/((x-3)(x^(2)-2x+1)) I have tried long division, simplifying it, and rearranging the equation. I ca      Log On


   

Question 773404: What is the domain and what are the zero(s) of the this function : (9x^(3)-4x)/((x-3)(x^(2)-2x+1))
I have tried long division, simplifying it, and rearranging the equation. I can't find any zero(s) or the domain. Please help!
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
%289x%5E%283%29-4x%29%2F%28%28x-3%29%28x%5E%282%29-2x%2B1%29%29

The domain is the set of acceptable values for x. The denominator of the function must not be zero, so looking at the two factors of the denominator, x%3C%3E3 and x%3C%3E1.
Note that x%5E2-2x%2B1=%28x-1%29%5E2.

Use the numerator to look for zeros of the function. This is x%289x%5E2-4%29, so this becomes zero when x=0 and when x=-sqrt%284%2F9%29 and x=sqrt%284%2F9%29; or stated more simply, the zeros of the function are x from the set { -2%2F3, 0, %2B2%2F3 }.