Systems of equations

Algebra Level 5

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

Let r,s,t,x,y,r, s, t, x, y, and zz be real numbers with r17r \neq 17 and x0x \neq 0 that satisfy the system of equations above.

Compute 1717r+3434s+8787t\dfrac {17}{17 - r}+\dfrac {34}{34 - s} + \dfrac {87}{87 - t}.

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