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

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

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

expand

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

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

Solution steps

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

Expand

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

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

x^{2} (cos (2 x + 3 y) (2 x + 3)) + sin (2 x + 3 y)

(x - 1) (e^{x} + 3)

x^{2} (x d v + v d x)

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

(x + y = z) (x + 2 x + z + 14)

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