<s>[INST] Simplify $\frac{x^3-x}{x^2+xy+x+y}$ $$\frac{x^3-x}{x^2+xy+x+y}$$
What I did:
 $$\frac{x}{xy+x+y}$$
through simplifying the $x$'s.
But it's not right.  
What did I do wrong?
 [/INST] You can only simplify factors of the numerator with factors of the denominator. Thus first you have to decompose the numerator and the denominator, and then simplify the fraction.

Start with
$$
\frac{x^3-x}{x^2+xy+x+y} = \frac{x(x^2-1)}{x(x+y)+x+y} = \frac{x(x+1)(x-1)}{(x+1)(x+y)},
$$
and now simplify the only common factor, that is $x+1$.
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