Question

Racionalize as frações:​

Answer 1

Resposta:

Explicação passo a passo:

$a)$

$\frac{1}{\sqrt{x} } =\frac{1.\sqrt{x} }{\sqrt{x} .\sqrt{x} } =\frac{\sqrt{x} }{\sqrt{x^{2} } } =\frac{\sqrt{x} }{x}$

$b)$

$\frac{2}{\sqrt{x} +\sqrt{4} }=\frac{2.(\sqrt{x} -\sqrt{4}) }{(\sqrt{x} +\sqrt{4}).(\sqrt{x} -\sqrt{4}) } =\frac{2.(\sqrt{x} -\sqrt{4}) }{(\sqrt{x}) ^{2}-(\sqrt{4}) ^{2} } =\frac{2.(\sqrt{x} -\sqrt{4}) }{(x-4)} =\frac{2.(\sqrt{x} -2)}{(x-4)}$

$c)$

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

$d)$

$\frac{4}{\sqrt[3]{x} } =\frac{4.\sqrt[3]{x^{2} } }{\sqrt[3]{x}.\sqrt[3]{x^{2} } } =\frac{4\sqrt[3]{x^{2} } }{\sqrt[3]{x^{3} } } =\frac{4\sqrt[3]{x^{2} } }{x}$