What is expand (2x^5+x^4+4x^3+3x^2-24x)/((x^2+1)^2) ?

The solution to expand (2x^5+x^4+4x^3+3x^2-24x)/((x^2+1)^2) is (2x^5+x^4+4x^3+3x^2-24x)/(x^4+2x^2+1)

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expand (2x^5+x^4+4x^3+3x^2-24x)/((x^2+1)^2)

expand

\frac{2 x ^{5} + x ^{4} + 4 x ^{3} + 3 x ^{2} - 24 x}{( x ^{2} + 1 ) ^{2}}

\frac{2 x ^{5} + x ^{4} + 4 x ^{3} + 3 x ^{2} - 24 x}{x ^{4} + 2 x ^{2} + 1}

Solution steps

\frac{2 x ^{5} + x ^{4} + 4 x ^{3} + 3 x ^{2} - 24 x}{( x ^{2} + 1 ) ^{2}}

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

= \frac{2 x ^{5} + x ^{4} + 4 x ^{3} + 3 x ^{2} - 24 x}{x ^{4} + 2 x ^{2} + 1}

(3 e + 6) (3 e - 6)

\frac{3 x ^{2} ( 3 x ^{2} + 2 x ^{4} )}{8}

\frac{( s + 2 )}{( s ^{2} + 4 s + 3 ) \cdot ( s + 5 )}

\frac{4 s + 1}{5 ( s ^{2} + 2 s + 2 )}

- \frac{( 5 x ^{2} + 3 x - 17 )}{( x ^{2} - 7 ) ( x + 6 )}

What is expand (2x^5+x^4+4x^3+3x^2-24x)/((x^2+1)^2) ?
The solution to expand (2x^5+x^4+4x^3+3x^2-24x)/((x^2+1)^2) is (2x^5+x^4+4x^3+3x^2-24x)/(x^4+2x^2+1)