Oh no not cubics!

Algebra Level 5

Let a,a, b,b, and cc be the roots of the cubic equation 7x314x2+21x28=0.7x^3-14x^2+21x-28=0. If abc,\dfrac{a}{bc} , bac,\dfrac{b}{ac}, and cab\dfrac{c}{ab} are the roots of the equation x3+rx2+sx+t,x^3+rx^2+sx+t, the value of rs\dfrac{r}{s} can be expressed as pq,-\dfrac{p}{q}, where pp and qq are coprime positive integers. Find p+q.p+q.

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