<s>[INST] Prove that $a+b+c\le 0$ $a,b,c$ are integer numbers different from zero and 
$$\frac{a}{b+c^2}=\frac{a+c^2}{b}$$
Prove that $a+b+c\le 0$.
I know how to prove that $a+b<0$ but do not know what about $c$.
 [/INST] We have $$ab=(a+c^2)(b+c^2)\\ab=ab+c^4+c^2(a+b)$$which means that $$a+b=-c^2\le -c$$or equivalently $$a+b+c\le 0$$
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