About a solution in Wolfram Alpha

Question

I'm intrigued by this finding on the extraordinary portal WolphramAlpha.

What is the reason why the solution has not been simplified, eliminating the factor $\frac{\sqrt x \sqrt{x+2}}{\sqrt {x(x+2)}} $? If not removal is justified, I would love to know why (I not discard that there is a strong and immediate reason, but I can not see it).

Answer 1

I think i's because you just don't know what $x$ is. It could be a complex number or an imaginary number.

Also, it could be zero the square root.

Answer 2

Because $\sqrt{x}\sqrt{x+2} \neq \sqrt{x(x+2)}$ for $x<-2$. This is easily seen by plugging in $x=-3$. On the left hand side, we get $$\sqrt{-3}\times\sqrt{-1} = \sqrt{3}i\times i=-\sqrt{3}$$ but on the right hand side, we get $\sqrt{-3(-1)}=\sqrt{3}$.