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

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

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

expand

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

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

Solution steps

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

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

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

(3 - \frac{x}{2})^{3}

6 (5 - 4)

\frac{( 4 x - 5 ) ( x + 1 )}{( 7 x + 8 ) ( x - 4 )}

\frac{sin ( x ) + tan ( x )}{tan ( x ) ( csc ( x ) + cot ( x ) )}

\frac{( 3 x ^{2} - 10 y ^{4} ) ^{2}}{16}

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