Question

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

Answer 1

0

Step-by-step explanation:

To Simplify:

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

How to Simplify:

1. All fraction contain different denominator, We have to Rationalize all.

2. Algebra Formula will use.

[a² - b² = (a + b)(a - b)]

3. After Rationalize get back to question and just add and subtract.

4. Get Answer

Solution:

Rationalizing of all terms see in attachment.

Now, Get back to the question,

$(2 \sqrt{3} + \sqrt{6} ) + (3 \sqrt{2} - 2 \sqrt{3} ) - (3 \sqrt{2} + \sqrt{6} ) \\ \\ = 2 \sqrt{3} + \sqrt{6} + 3 \sqrt{2} - 2 \sqrt{3} - 3 \sqrt{2} - \sqrt{6} \\ \\ = \cancel{2 \sqrt{3} } + \cancel{\sqrt{6} } + \cancel{3 \sqrt{2} } - \cancel{2 \sqrt{3} } - \cancel{3 \sqrt{2} } - \cancel{\sqrt{6}} \\ \\ = 0$

Therefore, The required answer is 0.

Answer 2

Answer: $3\sqrt{2}+\sqrt{6}$

Step-by-step explanation:

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

To find: Simplify the given expression.

Solution:

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

⇒ $\frac{3\sqrt{2} }{\sqrt{6}-\sqrt{3} } + \frac{2\sqrt{3}(\sqrt{6}-\sqrt{2} )-4\sqrt{3}(\sqrt{6}+\sqrt{2} ) }{(\sqrt{6})^{2} -(\sqrt{2})^{2} }$

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

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

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

⇒ $\frac{12\sqrt{2}- [\sqrt{6}(6\sqrt{2}+6\sqrt{6} ) -\sqrt{3} ((6\sqrt{2}+6\sqrt{6} )) }{4(\sqrt{6}-\sqrt{3} )}$

⇒ $\frac{12\sqrt{2}- [(6\sqrt{12}+36 ) - (6\sqrt{6}+6\sqrt{18} )}{4(\sqrt{6}-\sqrt{3} )}$

⇒ $\frac{12\sqrt{2}- 6\sqrt{12}-36 + 6\sqrt{6}+6\sqrt{18} }{4(\sqrt{6}-\sqrt{3} )}$

After solving the above equation we get, $3\sqrt{2}+\sqrt{6}$.

• Hence, the required answer is  $3\sqrt{2}+\sqrt{6}$.

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