SOLUTION: 5/3x-1 - x-7/9x^-1=-2/3x+1

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Question 174167: 5/3x-1 - x-7/9x^-1=-2/3x+1

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that the problem is actually:
5%2F%28%283x-1%29%29 - %28%28x-7%29%29%2F%28%289x%5E2-1%29%29 = -2%2F%28%283x%2B1%29%29
:
(9x^2-1) is difference of squares, factor this:
5%2F%28%283x-1%29%29 - %28%28x-7%29%29%2F%28%283x%2B1%29%283x%2B1%29%29 = -2%2F%28%283x%2B1%29%29
:
Multiply equation by (3x+1)(3x-1)
(3x+1)(3x-1)*5%2F%28%283x-1%29%29 - (3x+1)(3x-1)*%28%28x-7%29%29%2F%28%283x%2B1%29%283x%2B1%29%29 = (3x+1)(3x-1)*-2%2F%28%283x%2B1%29%29
:
Cancel out the denominators:
5(3x+1) - (x-7) = -2(3x-1)
:
15x + 5 - x + 7 = -6x + 2
:
14x + 12 = -6x + 2
:
14x + 6x = 2 - 12
:
20x = -10
x = %28-10%29%2F20
x = -1%2F2
:
You can check the solution in the original equation using x=-.5
5%2F%28%283%28-.5%29-1%29%29 - %28%28-.5-7%29%29%2F%28%289%28-.5%5E2%29-1%29%29 = -2%2F%28%283%28-.5%29%2B1%29%29