Question

Simplify 1+ root 2/ 1- root 3 + 1- root 2/ 1+ root 3

Answer 1

Answer :

–(1 + √6)

For explaination , please refer to the attachment .

Answer 2

The given question is

$\frac{1 + \sqrt{2} }{1 - \sqrt{3} } + \frac{1 - \sqrt{2} }{1 + \sqrt{3} }$

we have to simplify the above expression.

By normal addition we have to perform the steps.

The LCM of the expression is

$(1 - \sqrt{3} )(1 + \sqrt{3)}$

${1}^{2} - ( { \sqrt{3} }^{2} ) \\ 1 - 3 = - 2$

multiply both sides by

$\frac{1 + \sqrt{2} }{1 - \sqrt{3} } (1 + \sqrt{3} ) + \frac{(1 - \sqrt{2)} }{(1 + \sqrt{3} } (1 - \sqrt{3)}$

$\frac{(1 + \sqrt{2} + \sqrt{3} + \sqrt{6} + 1 - \sqrt{2} - \sqrt{3} + \sqrt{6}) }{ - 2}$

all the positive and negative terms will get cancelled. after that we get

$\frac{(1 + 1 + \sqrt{6} + \sqrt{6} ) }{ - 2 } \\ \frac{2 + 2 \sqrt{6} }{ - 2} \\ = \frac{2(1 + 1 \sqrt{6}) }{ - 2} \\ = - (1 + \sqrt{6} )$

Therefore, the final. answer is -(1+√6)

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