Systems of equations

Algebra Level 5

\begin{aligned} 17x + sy + tz = 0\\ rx + 34y + tz = 0\\ rx + sy + 87z = 0 \end{aligned}

Let $r, s, t, x, y,$ and $z$ be real numbers with $r \neq 17$ and $x \neq 0$ that satisfy the system of equations above.

Compute $\dfrac {17}{17 - r}+\dfrac {34}{34 - s} + \dfrac {87}{87 - t}$.

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