Hey,

       nivedh you are wrong. (x-3) can be greater than zero or less than it, there are two possibilities.

If x-1=0 , then the inequality holds true and x=1. Else

if x-1 is not equal to zero,

x²-4x+3=(x-1)(x-3) and the (x-1) in the numerator and denominator cancel each other.

So, weget 1/(x-3) < 1.          [ineq 1]

Now, if x-3>=0 i.e. x>=3,

from [ineq 1] we get x-3>1, i.e. x>4.

combining both we get x>4.

Again if x-3<0, i.e. x<3 ,

from [ineq 1] we get x-3<1 i.e. x<4.

combining both we get x<4.

Please do rate me.