SOLUTION: hey i need help solving this rational equation. Here it is: 1/x - 1/6 = 4/3x^2 Thank you!!

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Question 136585: hey i need help solving this rational equation.
Here it is:
1/x - 1/6 = 4/3x^2
Thank you!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx - 1%2F6 = 4%2F%283x%5E2%29
:
Multiply equation by a common denominator 6x^2
6x^2*1%2Fx - 6x^2*1%2F6 = 6x^2*4%2F%283x%5E2%29
:
Cancel out the denominators, leaving you with:
6x - x^2 = 2(4)
:
You can arrange this as a quadratic equation:
x^2 - 6x + 8 = 0
Factors to:
(x-2)(x-4) = 0
Solutions
x = 2, x = 4
:
Check solution using x = 4
1%2F4 - 1%2F6 = 4%2F%283%2A16%29
1%2F4 - 1%2F6 = 4%2F%2848%29
Using a common denominator of 12:
3%2F12 - 2%2F12 = 1%2F12
You can check the x = 2 solution