Question

Simplify \(\frac{(a^2 - \frac{1}{a}) (a^{\frac{4}{3}} + a^{\frac{2}{3}})}{a^2 - \frac{1}{a}^2}\)

A a^{\(\frac{2}{3}\)}
B a^{-\(\frac{1}{3}\)}
C \(a^{2}\) + 1
D a
E a^{\(\frac{1}{3}\)}

Answer 1

The correct answer is E. a^{\(\frac{1}{3}\)}

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

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