Value of $ \frac{a^2 + b^2 + c^2}{ac^2 - ab^2} $ If  $a + b + c = 0$ , then value of $ \frac{a^2 + b^2 + c^2}{ac^2 - ab^2} $ is?
According to me if $ a + b + c = 0$, then $a + b = -c$

This implies $ (a + b)^2 = c^2$
This implies $a^2 + b^2 = c^2 - 2ab$

Putting this value in  $ \frac{a^2 + b^2 + c^2}{ac^2 - ab^2} $ we get

$ \frac {c^2 - 2ab + c^2}{ac ^ 2 - ab}  = \frac {2c^2 - 2ab}{a(c^2 - b)} $
But I'm stuck after this. Am I right in the above steps, if yes, then how should I continue?


Note that in the denominator
$$ ac^2-ab^2=a(c+b)(c-b)=a^2(b-c)$$
for further simplification. Actually, since $a$ plays a special role in the original expresion, I suggest to simply eliminate $a$ by replacing it with $-(b+c)$ throughout, e.g.
$$\frac{a^2+b^2+c^2}{ac^2-ab^2}=\frac{2(b^2+bc+c^2)}{(b+c)(b^2-c^2)} $$
