Question

GENTE POR FAVOR ME AJUDEM

5/4-raiz de 3 - 1/4 + raiz de 3

Answer 1

$\frac{20-4+5 \sqrt{3}+ \sqrt{3} }{13}$$\frac{5}{4- \sqrt{3} } - \frac{1}{4+ \sqrt{3} }$

$( \frac{5}{4- \sqrt{3} } * \frac{4+ \sqrt{3} }{4+ \sqrt{3} } ) - (\frac{1}{4+ \sqrt{3} } * \frac{4- \sqrt{3} }{4- \sqrt{3} } )$

$\frac{20+5 \sqrt{3} }{16-3} - \frac{4- \sqrt{3} }{16-3}$


$\frac{20-4+5 \sqrt{3}+ \sqrt{3} }{13}$

$\frac{16+6 \sqrt{3} }{13}$

Answer 2

A $\sqrt{3}$ vai zerar com $-\sqrt{3}$, sobrando apenas as frações.
Segue resolução:
$\dfrac{5}{4}-\sqrt{3}-\dfrac{1}{4}+\sqrt{3}\\ (\sqrt{3}-\sqrt{3})+\dfrac{5}{4}-\dfrac{1}{4}\\ 0+\dfrac{5}{4}-\dfrac{1}{4} = \dfrac{5-1}{4} = \dfrac{4}{4} = 1$

Resolução extra:
$\dfrac{5}{4-\sqrt{3}}-\dfrac{1}{4+\sqrt{3}}\\\\\\ \dfrac{5(4+\sqrt{3})-1(4-\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}\\\\\\ \dfrac{20+5\sqrt{3}-4+\sqrt{3}}{(4-\sqrt{3})(4+\sqrt{3})}\\\\\\ \dfrac{20+5\sqrt{3}-4+\sqrt{3}}{16+4\sqrt{3}-4\sqrt{3}-3}\\\\\\ \boxed{\boxed{\dfrac{16+6\sqrt{3}}{13}}}$

Bons estudos!