You've made a mistake when you divided the expression with the term .
This is what you should do:
And now you see that the equality will hold if either or , that is if or Since you have a constraint the correct answer is
Because you cannot be sure whether or not you carried out a division by zero! For an example, if you want to divide something with an expression (x-1) than you should point out that you exclude the possibility of x taking the value 1, thus you loose a possible solution, which exactly was the case here. And I suspect that wast the idea of the given problem, to see if one is aware of what I just said in the first two sentences of this post.
As Mathoman said, you cannot divide by 0. What you could have done, rather than factor, was, at the point where you had
was think "If x- 1 is not 0, I can divide both sides by to get 3(x+ 1)= x- 1, 3x+ 3= x- 1, 2x= -4, x= -2. But if x- 1= 0, then both sides would equal 0 so x= 1 is also a solution."
If the condition "x> 0" had not been included, both x= -2 and x= 1 would have given stationary points. With that condition, only x= 1 does.