SOLUTION: solve for all values of x: x-1/x-5 - 1/5= 20/x^2-5x

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Question 950246: solve for all values of x: x-1/x-5 - 1/5= 20/x^2-5x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the equation is:
%28%28x-1%29%29%2F%28%28x-5%29%29+-+1%2F5+=+20%2F%28%28x%5E2-5x%29%29
Factor out x
%28%28x-1%29%29%2F%28%28x-5%29%29+-+1%2F5+=+20%2F%28x%28x-5%29%29
multiply by the common denominator 5x(x-5)
5x(x-5)*%28%28x-1%29%29%2F%28%28x-5%29%29 - 5x(x-5)*1%2F5 = 5x(x-5)*20%2F%28x%28x-5%29%29
cancel the denomonators
5x(x-1) - x(x-5) = 5(20)
5x^2 - 5x - x^2 + 5x = 100
Combine like terms
5x^2 - x^2 - 5x + 5x = 100
4x^2 = 100
x^2 = 100/4
x^2 = 25
x = +/-sqrt%2825%29
x = 5
or
x =-5
:
x = 5 cannot be a solution, we would have division by 0 in the original problem
however
x = -5 seems to work ok in the original problem, only solution