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

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

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

expand

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

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

Solution steps

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

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

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

Expand

x (x^{4} + 2 x^{2} + 1) : x^{5} + 2 x^{3} + x

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

(sin (2 x) + cos (2 x))^{2}

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

(2 + 7) \cdot 3

\frac{1}{s ( s - 1 )}

(2 - 1)^{5}

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