SOLUTION: how do you solve this equation? 1/x-1 + 2/x = x/x-1

Question 2506: how do you solve this equation?
1/x-1 + 2/x = x/x-1
Found 2 solutions by borzeya, kiru_khandelwal:
Answer by borzeya(6) (Show Source): You can put this solution on YOUR website!
[(1*(x))/((x-1)*(x))]+[(2*(x-1))/((x)*(x-1))]=[((x)*(x))/((x-1)*(x))]
[(3x-2)/(x^2-x)]=[(x^2)/(x^2-x)]
3x-2=x^2
x^2-3x+2=0
(x-2)(x-1)=0
x-2=0 => x=2; x-1=0 => x=1

Answer by kiru_khandelwal(79) (Show Source): You can put this solution on YOUR website!
1/(x-1) + 2/x = x/(x-1)
=> (x + 2(x-1))/x(x-1) = x/(x-1)
=> (3x-2)/x(x-1) = x/(x-1)
=> (3x-2)(x-1)/x(x-1) = x
=> (3x-2)/x = x
=> 3x-2 = x^2
=> x^2-3x+2 = 0
=> x^2-2x-x+2 = 0
=> x(x-2)-(x-2)=0
=> (x-1)(x-2)=0
According to the zero product rule
x=1,2
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