Question

dau coroana urgent :

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

Answer 1

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

$\green{(a + b)(a - b) = a {}^{2} - b {}^{2} }$

$\frac{2 \times 2+ 2 \sqrt{3} }{2 {}^{2} - \sqrt{3 } {}^{2} } - 3 - 2 \sqrt{3} = 1 \\ \\ \frac{4 + 2 \sqrt{3} }{4 - 3} - 3 - 2 \sqrt{3} = 1 \\ \\ \frac{4 + 2 \sqrt{3} }{1} -3 - 2 \sqrt{3} = 1 \\ \\ 4 + 2 \sqrt{3} - 3 - 2 \sqrt{3} = 1 \\ \\ 4 - 3 = 1 \\ \\ 1 = 1 \huge \: Adevarat$