# Oh no not cubics!

Algebra Level 4

Let $$a,$$ $$b,$$ and $$c$$ be the roots of the cubic equation $$7x^3-14x^2+21x-28=0.$$ If $$\dfrac{a}{bc} ,$$ $$\dfrac{b}{ac},$$ and $$\dfrac{c}{ab}$$ are the roots of the equation $$x^3+rx^2+sx+t,$$ the value of $$\dfrac{r}{s}$$ can be expressed as $$-\dfrac{p}{q},$$ where $$p$$ and $$q$$ are coprime positive integers. Find $$p+q.$$

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