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\frac{6\times \frac{\sqrt{5}}{\sqrt{3}}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.
\frac{6\times \frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\frac{6\times \frac{\sqrt{5}\sqrt{3}}{3}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
The square of \sqrt{3} is 3.
\frac{6\times \frac{\sqrt{15}}{3}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
\frac{2\sqrt{15}-10\sqrt{\frac{3}{5}}+2\sqrt{15}}{\sqrt{5}}
Cancel out 3, the greatest common factor in 6 and 3.
\frac{2\sqrt{15}-10\times \frac{\sqrt{3}}{\sqrt{5}}+2\sqrt{15}}{\sqrt{5}}
Rewrite the square root of the division \sqrt{\frac{3}{5}} as the division of square roots \frac{\sqrt{3}}{\sqrt{5}}.
\frac{2\sqrt{15}-10\times \frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+2\sqrt{15}}{\sqrt{5}}
Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\frac{2\sqrt{15}-10\times \frac{\sqrt{3}\sqrt{5}}{5}+2\sqrt{15}}{\sqrt{5}}
The square of \sqrt{5} is 5.
\frac{2\sqrt{15}-10\times \frac{\sqrt{15}}{5}+2\sqrt{15}}{\sqrt{5}}
To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.
\frac{2\sqrt{15}-2\sqrt{15}+2\sqrt{15}}{\sqrt{5}}
Cancel out 5, the greatest common factor in 10 and 5.
\frac{2\sqrt{15}}{\sqrt{5}}
Combine 2\sqrt{15} and -2\sqrt{15} to get 0.
\frac{2\sqrt{15}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{2\sqrt{15}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\frac{2\sqrt{15}\sqrt{5}}{5}
The square of \sqrt{5} is 5.
\frac{2\sqrt{5}\sqrt{3}\sqrt{5}}{5}
Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.
\frac{2\times 5\sqrt{3}}{5}
Multiply \sqrt{5} and \sqrt{5} to get 5.
2\sqrt{3}
Cancel out 5 and 5.