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})
Correct Answer: Option E
Explanation
(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})