Question

Me ajudem, não consigo resolver isso Obrigada!

Answer 1

$\frac{2+ \sqrt{3} }{1- \sqrt{5} } + \frac{2- \sqrt{3} }{1+ \sqrt{5} } =\\ \\ \frac{(1+ \sqrt{5} )(2+ \sqrt{3} )+(1- \sqrt{5} )(2- \sqrt{3} )}{(1- \sqrt{5} )(1+ \sqrt{5} )} =\\ \\ \frac{(2+ \sqrt{3}+2\sqrt{5}+\sqrt{6} )+(2- \sqrt{3}-2\sqrt{5}-\sqrt{6})}{1^2- (\sqrt{5})^2 } =\\ \\ \frac{2+2 +(\sqrt{3} -\sqrt{3})+(2 \sqrt{5}-2 \sqrt{5})+(\sqrt{6}-\sqrt{6} ) }{1-5}= \\ \\ \frac{2+2+0+0+0}{-4} = \\ \\ = \frac{4}{-4} = -1.$