# Christyan's rational expression

Algebra Level 4

Let $$u,v,w$$ be real numbers satisfying $$uvw=u+v+w=1$$ and $$u^2+v^2+w^2=2013$$. If $\dfrac{1}{uv+w}+\dfrac{1}{wu+v}+\dfrac{1}{vw+u} = -\frac{a}{b},$ where $$a$$ and $$b$$ are positive coprime integers, what is the value of $$a$$?

This problem is posed by Christyan Tamaro N.

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