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

The solution to expand ((2e^x+2e^2x)x)/((1+e^x)^2) is (2e^xx+2e^2x^2)/(1+2e^x+e^{2x)}

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

(2 x + y) (3 x - 5 y)

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

(- 1 + - 25 x^{2} - 10 x + 101)^{2}

\frac{5}{( x - 5 ) ( x ^{2} - 9 s + 20 )}

sec^{2} (x) (1 + cos (x))

What is expand ((2e^x+2e^2x)x)/((1+e^x)^2) ?
The solution to expand ((2e^x+2e^2x)x)/((1+e^x)^2) is (2e^xx+2e^2x^2)/(1+2e^x+e^{2x)}