Question

Simplify by rationalising the denominator:

3

5 − √3

+

2

5 + √3​

Answer 1

Given :  3/(5 - √3)  + 2/(5 + √3)

To Find : Simplify

Solution:

 3/(5 - √3)  + 2/(5 + √3)

= {3(5 + √3)  + 2(5 - √3)}/((5 - √3)/(5 + √3)

in denominator

(a - b)(a + b) = a² - b²

a = 5  b = √3

= { 15 + 3√3   + 10 - 2√3) /(25 - 3)

= ( 25  + √3)/22

= 25/22 + √3/22

3/(5 - √3)  + 2/(5 + √3) = 25/22 + √3/22  

Learn more:

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