SOLUTION: will you please answer this problem it will be very appricaited solve the equation or inequality x + 2x/x-2 = 3x-2/x-2

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Question 117340: will you please answer this problem it will be very appricaited

solve the equation or inequality
x + 2x/x-2 = 3x-2/x-2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+2x%2F%28x-2%29+=+3x+-+2%2F%28x-2%29
Right away I know that x cannot = 2 because division by 0
is not allowed and x-2+=+0
multiply both sides by x-2
x%28x-2%29+%2B+2x+=+3x%28x-2%29+-+2
x%5E2+-+2x+%2B+2x+=+3x%5E2+-+6x+-+2
2x%5E2+-+6x+-+2+=+0
x%5E2+-+3x+-+1+=+0
Using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
x+=+%283+%2B-+sqrt%289+%2B+4%29%29%2F2
x+=+%283+%2B+sqrt%2813%29%29%2F2
x+=+%283+-+sqrt%2813%29%29%2F2
I plugged one of these back into the original
problem, and it checked OK