<s>[INST] How can I simplify this fraction problem? I have the problem $\frac{x^2}{x^2-4} - \frac{x+1}{x+2}$ which should simplify to $\frac{1}{x-2}$
I have simplified $x^2-4$, which becomes:
$\frac{x^2}{(x-2)(x+2)} - \frac{x+1}{x+2}$
However, if I combine the fractions I get, $x^2-x-1$ for the numerator, which can't be factored. That's where I get stuck.
How can I get $\frac{1}{x-2}$ out of this problem?
 [/INST] You need to put them over a common denominator,
$$\frac {x+1}{x+2}=\frac {(x+1)(x-2)}{(x+2)(x-2)}=\frac {x^2-x-2}{x^2-4}$$
Now you can subtract the numerators
$$x^2-(x^2-x-2)=x+2$$
and finally divide out the $x+2$ from numerator and denominator  
Your $-1$ should be $-2$.  You didn't show your work, so I can't see why it happened.
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