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Popular >

expand (x-2/x)^{-3}

Solution

expand

(x - \frac{2}{x})^{- 3}

Solution

\frac{x ^{3}}{( x ^{2} - 2 ) ^{3}}

Solution steps

(x - \frac{2}{x})^{- 3}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( x - \frac{2}{x} ) ^{3}}

(x - \frac{2}{x})^{3} = \frac{( x ^{2} - 2 ) ^{3}}{x ^{3}}

= \frac{1}{\frac{( x ^{2} - 2 ) ^{3}}{x ^{3}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x ^{3}}{( x ^{2} - 2 ) ^{3}}

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Frequently Asked Questions (FAQ)

What is expand (x-2/x)^{-3} ?
The solution to expand (x-2/x)^{-3} is (x^3)/((x^2-2)^3)