Question

simplify : √5-2 / √5+2 - √5+2 / √5-2​

Answer 1

Your answer is in the attachment.....

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Answer 2

Answer:

$\bf \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } \\ \\ = \bf\frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2 } - \frac{ \sqrt{5} + 2}{ \sqrt{5} - 2 } \times \frac{ \sqrt{5} + 2 }{ \sqrt{5} + 2 } \\ \\ = \bf\frac{ {( \sqrt{5} - 2)}^{2} }{( \sqrt{5 } + 2)( \sqrt{5} - 2)} - \frac{ {( \sqrt{5} + 2) }^{2} }{ \sqrt{5} - 2)( \sqrt{5} + 2) } \\ \\ = \bf\frac{ { \sqrt{(5)} }^{2} + {2}^{2} - 2 \times 2 \times \sqrt{5} }{ {( \sqrt{5)} }^{2} - {2}^{2} } - \frac{ {( \sqrt{5)} }^{2} + {2}^{2} + 2 \times 2 \times \sqrt{5} }{ {( \sqrt{5)} }^{2} - {2}^{2} } \\ \\ = \bf\frac{5 + 4 - 4 \sqrt{5} }{5 - 4} - \frac{5 + 4 + 4 \sqrt{5} }{5 - 4} \\ \\ = \bf\frac{(9 - 4 \sqrt{5)} -(9 + 4 \sqrt{5)} }{5 - 4} \\ \\ = \bf\frac{9 - 4 \sqrt{5} - 9 - 4 \sqrt{5} }{1} \\ \\ = \bf - 4 \sqrt{5} - 4 \sqrt{5} \\ \\ = \sf- 8 \sqrt{5}$