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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

\frac{( a x + b )}{( c x + d )}

a (- 3, 2) y b (2, - 4)

\frac{1}{2} (- 2 x^{1} - x^{2} = 0)

\frac{2 ( 45 + 8885 )}{49}

\frac{32 ( x + 1 ) ( 2 x + 1 )}{3 x ^{2}}

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