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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

5 + 6

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

\frac{2 ( x + 9 ) ( x + 1 )}{( x + 4 ) ( x - 2 )}

x (x - 2 y)

\frac{d ^{3}}{d x ^{3}} ((y) (x^{10} - sec (x)))

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