tex]plzz..help me in solving this question.......

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June 2021 2 39 Report

rationalise the denominator of the following

[tex]1 \div \sqrt{7} - \sqrt{6} [/tex]
plzz..help me in solving this question....

Brainlytaj

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Question:-

Rationalise the denominator of the following

$\frac{1}{ \sqrt{7} - \sqrt{6} }$

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Answer is √7+√6

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Step by step explanation:-

$⇒ \frac{1}{ \sqrt{7} - \sqrt{6}} \\ \\ ⇒ \frac{1}{ \sqrt{7} - \sqrt{6} } \times \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} + \sqrt{6} } \\ \\ ⇒ \frac{ \sqrt{7} + \sqrt{6} }{( { \sqrt{7}) }^{2} {( \sqrt{6} }^{2} ) } \\ \\$

By using identity

${a}^{2} - {b}^{2} = (a + b)(a - b)$

So apply this identity in denominator ,

$⇒ \frac{ \sqrt{7} + \sqrt{6} }{ {( \sqrt{7} )}^{2} - {( \sqrt{6} )}^{2} } \\ \\⇒ \frac{ \sqrt{7} + \sqrt{6} }{7 - 6} \\ \\ ⇒ \sqrt{7} + \sqrt{6}$

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Question:-

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Answer is √7+√6

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