How to rationalize a denominator in a fraction? Like this. (((x)^(1/3) +2)/((x)^(1/3) −2))


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Question Number 56092 by Mikael_Marshall last updated on 10/Mar/19
$How to rationalize a denominator in a fraction? Like this. (((x)^(1/3) +2)/((x)^(1/3) −2))$
$H o w t o r a t i o n a l i z e a d e n o m i n a t o r i n$ $a f r a c t i o n ? L i k e t h i s .$ $\frac{\sqrt[3]{x} + 2}{\sqrt[3]{x} - 2}$
	Answered by math1967 last updated on 10/Mar/19

	$\frac{(^{3} \sqrt{x} + 2) (x^{\frac{2}{3}} + 2 \times^{3} \sqrt{x} + 2^{2})}{(^{3} \sqrt{x} - 2) (x^{\frac{2}{3}} + 2 \times^{3} \sqrt{x} + 2^{2})}$ $\frac{(^{3} \sqrt{x} + 2) (x^{\frac{2}{3}} + 2 \times^{3} \sqrt{x} + 4)}{x - 2} ★$ $★ (a^{3} - b^{3}) = (a - b) (a^{2} + a b + b^{2})$
	Commented by Mikael_Marshall last updated on 10/Mar/19

	$t h a n k s S i r$
	Answered by peter frank last updated on 10/Mar/19

	$a = \sqrt[3]{x}$ $\frac{a + 2}{a - 2} = \frac{{(a + 2)}^{2}}{a^{2} - 4} = \frac{a^{2} + 4 a + 4}{a^{2} - 4}$ $\frac{\sqrt[3]{x} + 4 (\sqrt[3]{x}) + 4}{{(\sqrt[3]{x})}^{2} - 4}$
	Commented by math1967 last updated on 10/Mar/19

	${(^{3} \sqrt{x})}^{2} = x^{\frac{2}{3}} i s i r r a t i o n a l$
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