Question

simplify = 6/2√3-√6+√6/√3+√2-4√3/√6-√2

Answer 1

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Answer 2

Answer:

The answer is 0.

Step-by-step explanation:

Here, the given expression is,

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

By rationalizing,

$=\frac{6}{2\sqrt{3}-\sqrt{6}}\times \frac{2\sqrt{3}+\sqrt{6}}{2\sqrt{3}+\sqrt{6}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}\times \frac{\sqrt{6}+\sqrt{2}}{\sqrt{6}+\sqrt{2}}$

$=\frac{6(2\sqrt{3}+\sqrt{6})}{6}+\frac{\sqrt{6}(\sqrt{3}-\sqrt{2})}{1}-\frac{4\sqrt{3}(\sqrt{6}+\sqrt{2})}{4}$

( (a+b)(a-b) = a² - b² )

$=2\sqrt{3}+\sqrt{6}+\sqrt{6}(\sqrt{3}-\sqrt{2})-\sqrt{3}(\sqrt{6}+\sqrt{2})$

$=2\sqrt{3}+\sqrt{6}+\sqrt{18}-\sqrt{12}-\sqrt{18}-\sqrt{6}$

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

( Because, √18 = √(9×2) = √9 × √2 = 3√2 and √12 = √(4×3) = √4 × √3 = 2√3 )

$=0$