What is expand (2x^2+2x+13)/((x-2)(x^2+1)^2) ?

The solution to expand (2x^2+2x+13)/((x-2)(x^2+1)^2) is (2x^2+2x+13)/(x^5+2x^3+x-2x^4-4x^2-2)

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expand (2x^2+2x+13)/((x-2)(x^2+1)^2)

expand

\frac{2 x ^{2} + 2 x + 13}{( x - 2 ) ( x ^{2} + 1 ) ^{2}}

\frac{2 x ^{2} + 2 x + 13}{x ^{5} + 2 x ^{3} + x - 2 x ^{4} - 4 x ^{2} - 2}

Solution steps

\frac{2 x ^{2} + 2 x + 13}{( x - 2 ) ( x ^{2} + 1 ) ^{2}}

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

= \frac{2 x ^{2} + 2 x + 13}{( x - 2 ) ( x ^{4} + 2 x ^{2} + 1 )}

Expand

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

= \frac{2 x ^{2} + 2 x + 13}{x ^{5} + 2 x ^{3} + x - 2 x ^{4} - 4 x ^{2} - 2}

\frac{s ^{2} + 7}{( s - 2 ) ^{2} ( s ^{2} + 10 s + 50 )}

- y^{2} (y - x^{4} - \frac{y ^{4}}{4})

(x - 4) (a x - 2 + 3 x - 6)

sin (π (2 n - 1))

(5 - 4 z i)^{2}

What is expand (2x^2+2x+13)/((x-2)(x^2+1)^2) ?
The solution to expand (2x^2+2x+13)/((x-2)(x^2+1)^2) is (2x^2+2x+13)/(x^5+2x^3+x-2x^4-4x^2-2)