Question

$\frac{ \sqrt{5 } - 2}{ \sqrt{5} + 2?} - \frac{ \sqrt{5} + 2}{ \sqrt{5} - 2}$
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Answer 1

Answer:

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Answer 2

Hii there

here is your answer

ATQ,

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

We need to rationalize it.....

So,

First

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

should be rationalised

=

$\frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2 }$

=

$\frac{ { (\sqrt{5} - 2)}^{2} }{5 - 4}$

now,

$5 + 4 - 20 = - 11$

Now , to rationalize the other number

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

=

$\frac{ \sqrt{5} + 2}{ \sqrt{5} - 2} \times \frac{ \sqrt{5} + 2}{ \sqrt{5} + 2 }$

=

$\frac{ {( \sqrt{5} + 2) }^{2} }{5 - 4}$

$5 + 2 + 20 = 27$

= Now,

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

So,

= -11-(27)

= -38

Hope it helped u

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