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

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

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

expand

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

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

Solution steps

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

Expand

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

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

\frac{6 s ^{2} - 13 s + 2}{s ( s ^{2} + 2 s + 5 )}

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

\frac{1}{( 1 + 2 m ) ^{3}}

(2 (y \cdot v) + 4 y) (d y \cdot v + y \cdot d v)

\frac{d}{d x} ((z) (x y + z^{3} x - 2 y z))

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