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