Question

a racionalização de 9/√3+1resulta em ?

Answer 1

$\dfrac{9}{\sqrt{3}+1}\\ \\ \\ =\dfrac{9 \cdot \left(\sqrt{3}-1 \right )}{\left(\sqrt{3}+1\right)\cdot\left(\sqrt{3}-1 \right )}\\ \\ \\ =\dfrac{9 \cdot \left(\sqrt{3}-1 \right )}{\left(\sqrt{3} \right )^{2}-\sqrt{3}+\sqrt{3}-1}\\ \\ \\ =\dfrac{9 \cdot \left(\sqrt{3}-1 \right )}{3-1}\\ \\ \\ =\boxed{\dfrac{9 \cdot \left(\sqrt{3}-1 \right )}{2}}$

Answer 2

$\dfrac{9}{ \sqrt{3}+1} \\ \\ \\ \dfrac{9 *(\sqrt{3}+1)}{ (\sqrt{3}+1)*(\sqrt{3}+1)} \\ \\ \\ \dfrac{9+9\sqrt{3}}{ 4+2\sqrt{3}} \\ \\ \\=> \dfrac{ - 9+9\sqrt{3}}{ 2}}$

Ou 

$\dfrac{9 *(\sqrt{3}+1)}{ 2}$