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

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

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

expand

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

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

Solution steps

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

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

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

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

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

(2 t + 1) e^{t}

(x + i) (x - i)

\frac{2 ( 8 - 19 )}{3}

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