SOLUTION: need help solving x/x-1 + 2/x=0

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Question 203143: need help solving x/x-1 + 2/x=0
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x-1%29+%2B+2%2Fx+=+0
Start by eliminating the fractions. This can be done by multiplying both sides of the equation by the Lowest Common Denominator. (We could also use the LCD to add the fractions but this way is faster.) The LCD of (x-1) and x is x(x-1) so this is what we will multiply by:
x%28x-1%29%2A%28x%2F%28x-1%29+%2B+2%2Fx%29+=+x%28x-1%29%280%29
The right side is easy. On the left side use the Distributive Property to multiply:
x%28x-1%29%2A%28x%2F%28x-1%29%29+%2B+x%28x-1%29%2A%282%2Fx%29+=+0
Now cancel the common factors:

which leaves:
x%2Ax+%2B+2%28x-1%29+=+0
Simplifying we get:
x%5E2+%2B+2x+-+2+=+0
This won't factor so we will use the quadratic formula x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29 which is based on the standard form: ax%5E2+%2B+bx+%2Bc:


So the solutions are: x+=+-1+%2B+sqrt%283%29 or x+=+-1+-+sqrt%283%29.