Question

simplify (2√6÷√2+√3)+(6√2÷√6+√3)-(8√3÷√6+√3)

Answer 1

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Answer 2

Answer:

$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{3}}=8-2\sqrt{6}-2\sqrt{2}$

Step-by-step explanation:

we have to simplify $\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{3}}$

we simplify by rationalizing the denominator of each term.

$\implies\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}\times\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}-\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}\times\frac{\sqrt{6}-\sqrt{3}}{\sqrt{6}-\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{3}}\times\frac{\sqrt{6}-\sqrt{3}}{\sqrt{6}-\sqrt{3}}$

$\implies\frac{4\sqrt{3}-6\sqrt{2}}{2-3}+\frac{12\sqrt{3}-6\sqrt{6}}{6-3}-\frac{24\sqrt{2}-24}{6-3}$

$\implies\frac{4\sqrt{3}-6\sqrt{2}}{-1}+\frac{12\sqrt{3}-6\sqrt{6}}{3}-\frac{24\sqrt{2}-24}{3}$

$\implies-4\sqrt{3}+6\sqrt{2}+4\sqrt{3}-2\sqrt{6}-8\sqrt{2}+8$

$\implies8-2\sqrt{6}-2\sqrt{2}$

Therefore, $\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{3}}=8-2\sqrt{6}-2\sqrt{2}$