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

The solution to expand (x^5+1)/(x(x-1)(x^2+1)^2) is (x^5+1)/(x^6+2x^4+x^2-x^5-2x^3-x)

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expand (x^5+1)/(x(x-1)(x^2+1)^2)

expand

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

\frac{x ^{5} + 1}{x ^{6} + 2 x ^{4} + x ^{2} - x ^{5} - 2 x ^{3} - x}

Solution steps

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

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

= \frac{x ^{5} + 1}{x ( x - 1 ) ( x ^{4} + 2 x ^{2} + 1 )}

Expand

x (x - 1) (x^{4} + 2 x^{2} + 1) : x^{6} + 2 x^{4} + x^{2} - x^{5} - 2 x^{3} - x

= \frac{x ^{5} + 1}{x ^{6} + 2 x ^{4} + x ^{2} - x ^{5} - 2 x ^{3} - x}

5 (x + y) - 6 x + y - 8

- \frac{4 ( - 1 ) ^{n}}{π ( 2 n + 1 ) ( 2 n - 1 )}

(1 - sin (x)) (1 + cos (x))

\frac{1}{( s + 10 ) ( s ^{2} + 2 s + 16 )}

3 \times 9

What is expand (x^5+1)/(x(x-1)(x^2+1)^2) ?
The solution to expand (x^5+1)/(x(x-1)(x^2+1)^2) is (x^5+1)/(x^6+2x^4+x^2-x^5-2x^3-x)