Question

Racionalizando o denominador e simplificando a expressão \frac{\sqrt{3}+3}{\sqrt{3}+1} obtemos:

Answer 1

$\mathsf{\dfrac{\sqrt{3}+3}{\sqrt{3}+1}=\dfrac{(\sqrt{3}+3)}{(\sqrt{3}+1)}.\dfrac{(\sqrt{3}-1)}{(\sqrt{3}-1)}}$

$\mathsf{\dfrac{3-\sqrt{3}+3\sqrt{3}-3}{(\sqrt{3})^2-1^2}=\dfrac{2\sqrt{3}}{3-1}=\dfrac{2\sqrt{3}}{2}}$

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{\dfrac{\sqrt{3}+3}{\sqrt{3}+1}=\sqrt{3}}}}}}$