Given, 1x^5(1+x^5)^1/5 (1+x^5)^1/5=((x+1)(x^4 x^3+x^2 x+1))^1/5 =1x^5((x+1)(x^4 x^3+x^2 x+1))^1/5 ...

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Multiplication of Rational Expressions

Evxpand: 1x5...

Question

Evxpand:
$\frac{1}{x^{5} (1 + x^{5})^{\frac{1}{5}}}$

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Solution

Given,

$\frac{1}{x^{5} {(1 + x^{5})}^{\frac{1}{5}}}$

${(1 + x^{5})}^{\frac{1}{5}} = {((x + 1) (x^{4} - x^{3} + x^{2} - x + 1))}^{\frac{1}{5}}$

$= \frac{1}{x^{5} {((x + 1) (x^{4} - x^{3} + x^{2} - x + 1))}^{\frac{1}{5}}}$

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