Let \(r,s\) and \(t\) be the roots of \(x^3+ x\sqrt{A} + x\sqrt{2A} + A =0\). Find
\[ \frac{(r+s+t)(r+s-t)}{r^2+s^2-t^2+2rs}\]
where \( 100 \leq A \leq -100\).
###### Image Credit: Wikimedia Francois Viete

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