Question

Simplify 1/( 2+√3) + 2/(√5- √3) + 1/(2-√5)

Answer 1

Answer:

0

Step-by-step explanation:

Rationalising each term, we get :-

$\frac{1}{2 + \sqrt{3} } = 2 - \sqrt{3} \: \: \: \: \: \: (multiplying \: numerator \: and \: denominator \: by \: 2 - \sqrt{3} )$

$\frac{2}{ \sqrt{5} - \sqrt{3} } = \sqrt{5} + \sqrt{3} \: \: \: \: \: \: \: (multiplying \: numerator \: and \: denominator \: by \: \sqrt{5} + \sqrt{3} )$

$\frac{1}{2 - \sqrt{5} } = - 2 - \sqrt{5} \: \: \: \: \: \: (multiplying \: numerator \: and \: denominator \: by \:2 + \sqrt{5} )$

Thus, the given expression will become,

$\frac{1}{2 + \sqrt{3} } + \frac{2}{ \sqrt{5} - \sqrt{3} } + \frac{1}{2 - \sqrt{5} } = 2 - \sqrt{3} + \sqrt{5} + \sqrt{3} - 2 - \sqrt{5} = 0$

Hope it'll help you.....