Question

simplify 1+√2/1-√3+1-√2/1+√3​

Answer 1

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