Problem Solving

Hello,

I am a little confused about inequalities. Could someone please help me with the following question?

x^2>x

I have two ways of solving this one and they both give me different answers, please let me know which one is the correct method and why.

Method 1
x^2>x
x^2-x>0
x(x-1)>0
This means either x and x-1 are both +ive or both -ive
Case 1 (both +ive)
x>0 and x-1>0
=> x>1
Case 2(both -ive)
x<0 and x-1<0
=> x<0 and x<1 hence x<0

Hence Method 1 gives me x>1 or x<0

Method 2
x^2>x
Consider x to be +ive, we can divide by x
x>1
conside x to be -ive, we divide by a -ive number and change the inequality
x<-1

Hence Method 2 gives me x>1 and x<-1

Please let me know which method is correct.

Thanks.