Question

Please answer the question

Answer 1

2/(√1+y)+(√1-y) is the correct answer

Answer 2

TO RATIONALISE THE NUMERATOR OF

$\frac{ \sqrt{1 + y} - \sqrt{1 - y} }{y}$

RATIONALISATION :-

For rationalising the numerator we should multiply the fraction with such a factor such that (a+b)(a-b) identity can be applied to remove the Square roots.

$\frac{ \sqrt{1 + y} - \sqrt{1 - y} }{y} \\ \\ \\ = \frac{ \sqrt{1 + y} - \sqrt{1 - y} }{y} \times \frac{ \sqrt{1 + y} + \sqrt{1 - y} }{ \sqrt{1 + y} + \sqrt{1 - y} } \\ \\ \\ = \frac{ {( \sqrt{1 + y} ) }^{2} - { (\sqrt{1 - y}) }^{2} }{y( \sqrt{1 + y} + \sqrt{1 - y})} \\ \\ \\ = \frac{1 + y - (1 - y)}{y( \sqrt{1 + y} + \sqrt{1 - y})} \\ \\ \\ = \frac{1 + y - 1 +y }{y( \sqrt{1 + y} + \sqrt{1 - y})} \\ \\ \\ = \frac{2y}{y( \sqrt{1 + y} + \sqrt{1 - y})} \\ \\ \\ = \boxed{ \frac{2}{ \sqrt{1 + y} + \sqrt{1 - y}} }$

[ANS]

But we should multiply the same factor in denominator also so as the value remain same.