# Remarkable Question

Algebra Level 2

$\large \dfrac1{a+bc} +\dfrac1{b+ac} + \dfrac1{c+ab} = \dfrac x{ \left(1 + \frac ab\right)\left(1 + \frac bc\right)\left(1 + \frac ca\right) }$

Let $$a,b$$ and $$c$$ be positive real numbers satisfying $$\dfrac1a + \dfrac1b + \dfrac1c = 1$$, find the value of $$x$$ satisfying the algebraic identity above.

×