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algebra intermediate

Problem

When simplified, the third term in the expansion of

(\frac{a}{x} - \frac{x}{a ^{2}})^{6}

is:

(A)

\frac{15}{x}

(B)

- \frac{15}{x}

(C)

- \frac{6 x ^{2}}{a ^{9}}

(D)

\frac{20}{a ^{3}}

Solution

By the Binomial Theorem, the third term in the expansion is

(2 6) (\frac{a}{x})^{4} (\frac{- x}{a ^{2}})^{2}

15 \cdot \frac{a ^{4}}{x ^{2}} \cdot \frac{x}{a ^{4}}

\frac{15}{x}

The answer is

\frac{15}{x}

.

Final answer

A