How does this simplify to 1? I am working on this differetiation problem:
$ \frac{d}{dx}x(1-\frac{2}{x})$
and I am currently stuck at this point:
$1\cdot \left(1-\frac{2}{x}\right)+\frac{2}{x^2}x$
Symbolab tells me this simplifies to $1$ but I do not understand how. I am under the impression that;
$1\cdot \left(1-\frac{2}{x}\right)+\frac{2}{x^2}x \equiv 1- 2x^{-x^2}-2^{-x}$

Do not get confused by fractions and exponents.
You should remember that $\frac {k}{n} = kn^{-1}$ and not $k^{-n} $ and that $\frac {k}{n} l = kln^{-1}$ and not $kl^{-n} $.
We have $$1\times (1-\frac {2}{x}) = 1-\frac {2}{x} \tag {1}$$ and then $$\frac {2}{x^2}x = \frac {2}{x^2} \times x = \frac {2}{x} \tag {2} $$ 
What do we get by adding $(1)$ and $(2)$? The result is $1-\frac {2}{x} + \frac {2}{x} = 1$. Hope it helps. 
