What is expand (derivative of 2x(2-x))/((1+x)^2) ?

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

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expand (derivative of 2x(2-x))/((1+x)^2)

expand

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

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

Solution steps

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

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

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

Expand

2 x (2 - x) : 4 x - 2 x^{2}

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

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

(x + i y)^{3} - 2 (x + i y) + 6

(x - 1 + i) (x - 1 - i)

3 x (x y - 2) d x + (x^{3} + 2 y) d y

\frac{x ^{2} - 5 x + 16}{( 2 x + 1 ) ( x - 2 ) ^{2}}

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