What is expand ((5x^2-1)^3)/(30x) ?

The solution to expand ((5x^2-1)^3)/(30x) is (25x^5)/6-(5x^3)/2+x/2-1/(30x)

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expand ((5x^2-1)^3)/(30x)

expand

\frac{( 5 x ^{2} - 1 ) ^{3}}{30 x}

\frac{25 x ^{5}}{6} - \frac{5 x ^{3}}{2} + \frac{x}{2} - \frac{1}{30 x}

Solution steps

\frac{( 5 x ^{2} - 1 ) ^{3}}{30 x}

(5 x^{2} - 1)^{3} = 125 x^{6} - 75 x^{4} + 15 x^{2} - 1

= \frac{125 x ^{6} - 75 x ^{4} + 15 x ^{2} - 1}{30 x}

Apply the fraction rule:

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

\frac{125 x ^{6} - 75 x ^{4} + 15 x ^{2} - 1}{30 x} = \frac{125 x ^{6}}{30 x} - \frac{75 x ^{4}}{30 x} + \frac{15 x ^{2}}{30 x} - \frac{1}{30 x}

= \frac{125 x ^{6}}{30 x} - \frac{75 x ^{4}}{30 x} + \frac{15 x ^{2}}{30 x} - \frac{1}{30 x}

Cancel

\frac{125 x ^{6}}{30 x} : \frac{25 x ^{5}}{6}

= \frac{25 x ^{5}}{6} - \frac{75 x ^{4}}{30 x} + \frac{15 x ^{2}}{30 x} - \frac{1}{30 x}

Cancel

\frac{75 x ^{4}}{30 x} : \frac{5 x ^{3}}{2}

= \frac{25 x ^{5}}{6} - \frac{5 x ^{3}}{2} + \frac{15 x ^{2}}{30 x} - \frac{1}{30 x}

Cancel

\frac{15 x ^{2}}{30 x} : \frac{x}{2}

= \frac{25 x ^{5}}{6} - \frac{5 x ^{3}}{2} + \frac{x}{2} - \frac{1}{30 x}

2 - x ((1 - x) (2 - x))

e^{x + y} (- e^{- x - y} + e^{- x})

\frac{3 ( a + b )}{z + 2 ( a + b )}

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

- cos (3 (1 + 3 X^{2}))

What is expand ((5x^2-1)^3)/(30x) ?
The solution to expand ((5x^2-1)^3)/(30x) is (25x^5)/6-(5x^3)/2+x/2-1/(30x)