Question

simplify the following: √5-2/√5+ 2 ÷√5 + 2/ √5- 2

Answer 1

First we rationalise both term separately. Then at numerator use second and first identity respectively. Then at denominator we use third identity.

Hope its help u..

Answer 2

Hi there !

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Given :

$\bold{ \huge{ \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } - \frac{ \sqrt{5} + 2 }{ \sqrt{5} - 2 } }}$

Solution ;

On rationalising it's denominator :

$</p> <p>\frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } - \frac{ \sqrt{5} + 2 }{ \sqrt{5} - 2 } \\ \\ \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } \times \frac{ \sqrt{5} - 2 }{ \sqrt{5} - 2 } - \frac{ \sqrt{5} + 2 }{ \sqrt{5} - 2 } \times \frac{ \sqrt{5} + 2 }{ \sqrt{5} + 2 } \\ \\ \frac{( \sqrt{5} - 2) {}^{2} }{( \sqrt{5}) {}^{2} - (2) {}^{2} } - \frac{( \sqrt{5} + 2) {}^{2} }{( \sqrt{5}) {}^{2} - (2) {}^{2} } \\ \\ \frac{5 + 4 - 4 \sqrt{5} }{5 - 4} - \frac{5 + 4 + 4 \sqrt{5} }{5 - 4} \\ \\ \frac{9 - 4 \sqrt{5} }{1} - \frac{9 + 4 \sqrt{5} }{1} \\ \\ \cancel9 - 4 \sqrt{5} - \cancel 9 - 4 \sqrt{5} \\ \\ \bold{ \huge {- 8 \sqrt{5} }}$

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Thanks for the question !