Question

Solve :
(√5 - 2)/(√5 + 2) - (√5 + 2)/(√5 - 2)

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{5} - 2}{ \sqrt{5} + 2} - \frac{ \sqrt{5} + 2}{ \sqrt{5} - 2 } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2 }{ \sqrt{5} - 2} - \frac{ \sqrt{5} + 2 }{ \sqrt{5} - 2 } \times \frac{ \sqrt{5} + 2 }{ \sqrt{5} + 2 } \\ \\ = \frac{ {( \sqrt{5}) }^{2} + {(2)}^{2} - 2 \times \sqrt{5} \times 2 }{ {( \sqrt{5}) }^{2} - {(2)}^{2} } - \frac{ {( \sqrt{5}) }^{2} + {(2)}^{2} + 2 \times \sqrt{5} \times 2 }{ {( \sqrt{5} )}^{2} - {(2)}^{2} } \\ \\ = \frac{5 + 4- 4\sqrt{5} }{5 - 4} - \frac{5 + 4 + 4 \sqrt{5} }{5 - 4} \\ \\ = (9 - 4 \sqrt{5} ) - (9 + 4 \sqrt{5} ) \\ \\ = 9 - 4 \sqrt{5} - 9 - 4 \sqrt{5} \\ \\ = - 4 \sqrt{5} - 4 \sqrt{5} \\ \\ = - 8 \sqrt{5}$

Hope this helps!!!!

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