<s>[INST] Simplifying $\frac{b^2+c^2-a^2}{(a-b)(a-c)}+\frac{c^2+a^2-b^2}{(b-c)(b-a)}+\frac{a^2+b^2-c^2}{(c-a)(c-b)}$ 
Simplify $$\frac{b^2+c^2-a^2}{(a-b)(a-c)}+\frac{c^2+a^2-b^2}{(b-c)(b-a)}+\frac{a^2+b^2-c^2}{(c-a)(c-b)}\,.$$

I tried very hard but I am not being able to solve it easily I opened up everything and multiplied all of it and got the answer -2. But it took me 1 hour and I also made many silly mistakes. Is there a quicker way than brute force?
 [/INST] hint
Multiply the first term by $ b-c$ to get in the numerator
$$b^3+c^2b-a^2b-b^2c-c^3+a^2c$$
and the others, by permutation
$$c^3+a^2c-b^2c-c^2a-a^3+b^2a$$
$$a^3+b^2a-c^2a-a^2b-b^3+c^2b$$
The result is $  -2$.
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