solve the eq |x/x-1|+|x|=x^2/|x-1|

Dear akash

|x/x-1|+|x|=x^2/|x-1|

|x| + |x||x-1|=x²

condition x can be equal to 1 because x-1 is on denominator

case 1 x<0

-x +x²-x  =x²

 x=0   which is not  a solution

case 2      0≤x<1

 x -(x)(x-1) =x² 

 x(x-1)=0

 x=0 and 1

 x=1 is not a solution

case 3    1<x

x+x(x-1) =x²

x²  =x^{2  which is always true} 

^{so final solution          x=0   and x>1}

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