How-to-rationalize-a-denominator-in-a-fraction-Like-this-x-1-3-2-x-1-3-2-

Question Number 56092 by Mikael_Marshall last updated on 10/Mar/19

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