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

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

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

expand

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

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

Solution steps

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

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

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

(2 + x - x^{2})^{6}

(2 x y + y) d x + (x^{2} - x) d y

\frac{sin ^{2} ( x )}{( 1 - cos ( x ) ) ^{2}}

(2 b + 3)^{2}

(1 + x + x^{2})^{5}

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