Question

Help with number (ii) please

Answer 1

Answer:

4/12-4 - 9/12+4 now solve it you get answer I think hope it's helpful for you

Answer 2

$\large\sf\underline{Given\::}$

Expression :

• $\bf\:\frac{ \sqrt{2} }{ \sqrt{6} - \sqrt{2} } - \frac{ \sqrt{3} }{ \sqrt{6} + \sqrt{ 2} }$

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$\large\sf\underline{Solution\::}$

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

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• LCM of (√6 - √2) and (√6 + √2) = (√6 - √2) (√6 + √2)

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$\sf\implies\: \frac{[ \sqrt{2} \times ( \sqrt{6} + \sqrt{2} )] -[\sqrt{3} \times ( \sqrt{6} - \sqrt{2}) ]}{( \sqrt{6} - \sqrt{2} )( \sqrt{6} + \sqrt{2}) }$

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• Multiplying the terms and removing the brackets in numerator

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$\sf\implies\: \frac{[\sqrt{12} + \sqrt{4} ] -[\sqrt{18} - \sqrt{6}]}{( \sqrt{6} - \sqrt{2} )( \sqrt{6} + \sqrt{2}) }$

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• We can use an identity in the denominator

Identity to be used :

$\maltese\bf\color{aqua}{(a+b) (a-b) =a^{2}-b^{2}}$

Here :

• a = $\color{blue}{\sqrt{6}}$

• b = $\color{blue}{\sqrt{2}}$

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$\sf\implies\: \frac{[\sqrt{12} + \sqrt{4} ] -[\sqrt{18} - \sqrt{6}]}{( \sqrt{6})^{2} - (\sqrt{2}) ^{2} }$

$\sf\implies\: \frac{[\sqrt{2 \times 2 \times 3} + \sqrt{2 \times 2} ] -[\sqrt{2 \times 3 \times 3} - \sqrt{6}]}{6 - 2 }$

$\sf\implies\: \frac{[2\sqrt{3}+2] -[3\sqrt{2} - \sqrt{6}]}{4}$

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• Removing the brackets

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$\small{\underline{\boxed{\mathrm\red{\implies\: \frac{2\sqrt{3} + 2 -3\sqrt{2}+ \sqrt{6}}{4} }}}}$ ★

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Now it can't be simplified further since we can't calculate the numbers with dissimilar irrational part .

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!! Hope it helps !!