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\frac{-\sqrt{9}}{3\sqrt{8}}
Divide -\frac{1}{3} by \frac{\sqrt{8}}{\sqrt{9}} by multiplying -\frac{1}{3} by the reciprocal of \frac{\sqrt{8}}{\sqrt{9}}.
\frac{-3}{3\sqrt{8}}
Calculate the square root of 9 and get 3.
\frac{-3}{3\times 2\sqrt{2}}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
\frac{-3}{6\sqrt{2}}
Multiply 3 and 2 to get 6.
\frac{-3\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}
Rationalize the denominator of \frac{-3}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{-3\sqrt{2}}{6\times 2}
The square of \sqrt{2} is 2.
\frac{-\sqrt{2}}{2\times 2}
Cancel out 3 in both numerator and denominator.
\frac{-\sqrt{2}}{4}
Multiply 2 and 2 to get 4.