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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

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

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