What is expand ((1+x^{-1})^3)/(-3) ?

The solution to expand ((1+x^{-1})^3)/(-3) is -1/3-1/x-1/(x^2)-1/(3x^3)

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expand ((1+x^{-1})^3)/(-3)

expand

\frac{( 1 + x ^{- 1} ) ^{3}}{- 3}

- \frac{1}{3} - \frac{1}{x} - \frac{1}{x ^{2}} - \frac{1}{3 x ^{3}}

Solution steps

\frac{( 1 + x ^{- 1} ) ^{3}}{- 3}

Apply the fraction rule:

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

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

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

= - \frac{\frac{x ^{3} + 3 x ^{2} + 3 x + 1}{x ^{3}}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= - \frac{x ^{3} + 3 x ^{2} + 3 x + 1}{3 x ^{3}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Remove parentheses:

(a) = a

= - \frac{x ^{3}}{x ^{3} \cdot 3} - \frac{3 x ^{2}}{x ^{3} \cdot 3} - \frac{3 x}{x ^{3} \cdot 3} - \frac{1}{x ^{3} \cdot 3}

Cancel

\frac{x ^{3}}{x ^{3} \cdot 3} : \frac{1}{3}

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

Cancel

\frac{3 x ^{2}}{x ^{3} \cdot 3} : \frac{1}{x}

= - \frac{1}{3} - \frac{1}{x} - \frac{3 x}{3 x ^{3}} - \frac{1}{3 x ^{3}}

Cancel

\frac{3 x}{x ^{3} \cdot 3} : \frac{1}{x ^{2}}

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

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

(0, - 7) y (4, 0)

\frac{2 + 5 s}{2 s ( 4 s ^{2} - s )}

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

What is expand ((1+x^{-1})^3)/(-3) ?
The solution to expand ((1+x^{-1})^3)/(-3) is -1/3-1/x-1/(x^2)-1/(3x^3)