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

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

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expand (2x)/((1-(1-x)^2)^2)

expand

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

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

Solution steps

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

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

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

Factor

x^{4} - 4 x^{3} + 4 x^{2} : x^{2} (x^{2} - 4 x + 4)

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

Cancel the common factor:

x

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

Expand

x (x^{2} - 4 x + 4) : x^{3} - 4 x^{2} + 4 x

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

\frac{5 ( 8 + 19 )}{6}

\frac{\partial}{\partial y} ((x) (4 x^{2} y + 3 y - 5))

(\frac{1}{s - 2} + 1) (s - 3)

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

(20 b d z + 32 c g a) + k (20 b d z + 32 c g a)

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