What is expand (3x^2-27x^4)/(x^3) ?

The solution to expand (3x^2-27x^4)/(x^3) is -27x+3/x

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expand (3x^2-27x^4)/(x^3)

expand

\frac{3 x ^{2} - 27 x ^{4}}{x ^{3}}

- 27 x + \frac{3}{x}

Solution steps

\frac{3 x ^{2} - 27 x ^{4}}{x ^{3}}

Factor

3 x^{2} - 27 x^{4} : 3 x^{2} (1 - 9 x^{2})

= \frac{3 x ^{2} ( 1 - 9 x ^{2} )}{x ^{3}}

Cancel

\frac{3 x ^{2} ( 1 - 9 x ^{2} )}{x ^{3}} : \frac{3 ( - 9 x ^{2} + 1 )}{x}

= \frac{3 ( - 9 x ^{2} + 1 )}{x}

Expand

3 (- 9 x^{2} + 1) : - 27 x^{2} + 3

= \frac{- 27 x ^{2} + 3}{x}

Apply the fraction rule:

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

\frac{- 27 x ^{2} + 3}{x} = - \frac{27 x ^{2}}{x} + \frac{3}{x}

= - \frac{27 x ^{2}}{x} + \frac{3}{x}

Cancel

\frac{27 x ^{2}}{x} : 27 x

= - 27 x + \frac{3}{x}

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What is expand (3x^2-27x^4)/(x^3) ?
The solution to expand (3x^2-27x^4)/(x^3) is -27x+3/x