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\frac{\sqrt{11}}{\sqrt{9}}-\sqrt{\frac{1}{9}}
Rewrite the square root of the division \sqrt{\frac{11}{9}} as the division of square roots \frac{\sqrt{11}}{\sqrt{9}}.
\frac{\sqrt{11}}{3}-\sqrt{\frac{1}{9}}
Calculate the square root of 9 and get 3.
\frac{\sqrt{11}}{3}-\frac{1}{3}
Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.
\frac{\sqrt{11}-1}{3}
Since \frac{\sqrt{11}}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.