What is expand ((x^2+1)(x^4-x^2+1))/(2x^3) ?

The solution to expand ((x^2+1)(x^4-x^2+1))/(2x^3) is (x^3)/2+1/(2x^3)

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expand ((x^2+1)(x^4-x^2+1))/(2x^3)

expand

\frac{( x ^{2} + 1 ) ( x ^{4} - x ^{2} + 1 )}{2 x ^{3}}

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

Solution steps

\frac{( x ^{2} + 1 ) ( x ^{4} - x ^{2} + 1 )}{2 x ^{3}}

Expand

(x^{2} + 1) (x^{4} - x^{2} + 1) : x^{6} + 1

= \frac{x ^{6} + 1}{2 x ^{3}}

Apply the fraction rule:

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

\frac{x ^{6} + 1}{2 x ^{3}} = \frac{x ^{6}}{2 x ^{3}} + \frac{1}{2 x ^{3}}

= \frac{x ^{6}}{2 x ^{3}} + \frac{1}{2 x ^{3}}

Cancel

\frac{x ^{6}}{2 x ^{3}} : \frac{x ^{3}}{2}

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

\frac{( 2 x + 3 ) ( x - 6 )}{( x + 2 ) ( x - 1 )}

\frac{4}{( x - 3 ) ( x + 1 )}

(\frac{5}{x + 2} + \frac{12}{x ^{2} - 4} + \frac{3}{2 - x}) (x + 2)

\frac{x + 1}{x ( x - 2 )}

(e^{3 x} + 4 e^{- 2 x})^{2}

What is expand ((x^2+1)(x^4-x^2+1))/(2x^3) ?
The solution to expand ((x^2+1)(x^4-x^2+1))/(2x^3) is (x^3)/2+1/(2x^3)