Question
Simplify: $\frac{2\sqrt{30}}{\sqrt{6}}-\frac{3\sqrt{140}}{\sqrt{28}}+\frac{\sqrt{55}}{\sqrt{99}}$
✓
Answer
$\frac{2\sqrt{30}}{\sqrt{6}}-\frac{3\sqrt{140}}{\sqrt{28}}+\frac{\sqrt{55}}{\sqrt{99}}$
$=\frac{2\sqrt{6\times5}}{\sqrt{6}}-\frac{3\sqrt{28\times5}}{\sqrt{28}}+\frac{\sqrt{11\times5}}{\sqrt{11\times9}}$
$=\frac{2\sqrt{6}\times\sqrt{5}}{\sqrt{6}}-\frac{3\sqrt{28}\times\sqrt{5}}{\sqrt{28}}+\frac{\sqrt{11}\times\sqrt{5}}{3\sqrt{11}}$
$=2\sqrt{5}-3\sqrt{5}+\frac{\sqrt{5}}{3}$
$=-\sqrt{5}+\frac{\sqrt{5}}{3}$
$=\frac{-3\sqrt{5}+\sqrt{5}}{3}$
$=\frac{-2\sqrt{5}}{3}$
$=\frac{2\sqrt{6\times5}}{\sqrt{6}}-\frac{3\sqrt{28\times5}}{\sqrt{28}}+\frac{\sqrt{11\times5}}{\sqrt{11\times9}}$
$=\frac{2\sqrt{6}\times\sqrt{5}}{\sqrt{6}}-\frac{3\sqrt{28}\times\sqrt{5}}{\sqrt{28}}+\frac{\sqrt{11}\times\sqrt{5}}{3\sqrt{11}}$
$=2\sqrt{5}-3\sqrt{5}+\frac{\sqrt{5}}{3}$
$=-\sqrt{5}+\frac{\sqrt{5}}{3}$
$=\frac{-3\sqrt{5}+\sqrt{5}}{3}$
$=\frac{-2\sqrt{5}}{3}$
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