Question

Resoluçao pfvr, estou à um dia tentando resolver mas n consigo chegar na alternativa D que é a rsposta segundo o livro​

Answer 1

$\dfrac{2}{\sqrt{5}-\sqrt{3}}-\dfrac{2}{\sqrt[3]{2}}$

Racionalizando ambas as frações, temos:

$\dfrac{2}{\sqrt{5}-\sqrt{3}}\cdot\left(\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}\right)-\dfrac{2}{\sqrt[3]{2}}\cdot\left(\dfrac{\sqrt[3]{2^2}}{\sqrt[3]{2^2}}\right)\\\\\dfrac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}-\dfrac{2\sqrt[3]{4}}{\sqrt[3]{2\cdot2^2}}\\\\\dfrac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5})^2-(\sqrt{3})^2}-\dfrac{2\sqrt[3]{4}}{\sqrt[3]{2^{2+1}}}\\\\\dfrac{2(\sqrt{5}+\sqrt{3})}{5-3}-\dfrac{2\sqrt[3]{4}}{\sqrt[3]{2^3}}$

$\dfrac{2(\sqrt{5}+\sqrt{3})}{2}-\dfrac{2\sqrt[3]{4}}{2}\\\\\boxed{\boxed{\sqrt{5}+\sqrt{3}-\sqrt[3]{4}}}$