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1-\frac{\sqrt{31}}{\sqrt{3}}
Rewrite the square root of the division \sqrt{\frac{31}{3}} as the division of square roots \frac{\sqrt{31}}{\sqrt{3}}.
1-\frac{\sqrt{31}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{\sqrt{31}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
1-\frac{\sqrt{31}\sqrt{3}}{3}
The square of \sqrt{3} is 3.
1-\frac{\sqrt{93}}{3}
To multiply \sqrt{31} and \sqrt{3}, multiply the numbers under the square root.
\frac{3}{3}-\frac{\sqrt{93}}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.
\frac{3-\sqrt{93}}{3}
Since \frac{3}{3} and \frac{\sqrt{93}}{3} have the same denominator, subtract them by subtracting their numerators.