jmc

Notice that $8=2\cdot 2^2$, $50=2\cdot 5^2$, and $18=2\cdot 3^2$. Thus, $\sqrt{8}+\sqrt{50}+\sqrt{18}$ simplifies to $2\sqrt{2}+5\sqrt{2}+3\sqrt{2}=10\sqrt{2}$. To rationalize the denominator of $\frac{1}{10\sqrt{2}}$, simply multiply top and bottom by $\sqrt{2}$ to get $\frac{\sqrt{2}}{10\cdot 2}=\boxed{\frac{\sqrt{2}}{20}}$.