Question

Me ajudem por favor
2-√3 sobre 2+√3

Answer 1

$\frac{2-\sqrt{3}}{2+\sqrt{3}} \times \frac{2+\sqrt{3}}{2+\sqrt{3}} =\frac{2^2-3}{(2+\sqrt{3})^2} \\\\\frac{1}{(2+\sqrt{3})^2} =\frac{1}{7+4\sqrt{3}} \\\\\frac{1}{7+4\sqrt{3}} \times\frac{7-4\sqrt{3}}{7-4\sqrt{3}} = \frac{7-4\sqrt{3}}{7^2-(4^2\times3)} = \frac{7-4\sqrt{3}}{49-48} = \\\\\boxed{7-4\sqrt{3}}$