What is expand (5x^3+4x^2+7x+3)/((x^2+2x+2)(x^2-x-1)) ?

The solution to expand (5x^3+4x^2+7x+3)/((x^2+2x+2)(x^2-x-1)) is (5x^3+4x^2+7x+3)/(x^4+x^3-x^2-4x-2)

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expand (5x^3+4x^2+7x+3)/((x^2+2x+2)(x^2-x-1))

expand

\frac{5 x ^{3} + 4 x ^{2} + 7 x + 3}{( x ^{2} + 2 x + 2 ) ( x ^{2} - x - 1 )}

\frac{5 x ^{3} + 4 x ^{2} + 7 x + 3}{x ^{4} + x ^{3} - x ^{2} - 4 x - 2}

Solution steps

\frac{5 x ^{3} + 4 x ^{2} + 7 x + 3}{( x ^{2} + 2 x + 2 ) ( x ^{2} - x - 1 )}

Expand

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

= \frac{5 x ^{3} + 4 x ^{2} + 7 x + 3}{x ^{4} + x ^{3} - x ^{2} - 4 x - 2}

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

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

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

cos (\frac{( 2 n + 1 ) π}{2})

What is expand (5x^3+4x^2+7x+3)/((x^2+2x+2)(x^2-x-1)) ?
The solution to expand (5x^3+4x^2+7x+3)/((x^2+2x+2)(x^2-x-1)) is (5x^3+4x^2+7x+3)/(x^4+x^3-x^2-4x-2)