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

The solution to expand (4e^x(-e^x+4))/((4+e^x)^3) is (-4e^{2x}+16e^x)/(64+48e^x+12e^{2x)+e^{3x}}

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expand (4e^x(-e^x+4))/((4+e^x)^3)

expand

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

\frac{- 4 e ^{2 x} + 16 e ^{x}}{64 + 48 e ^{x} + 12 e ^{2 x} + e ^{3 x}}

Solution steps

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

(4 + e^{x})^{3} = 64 + 48 e^{x} + 12 e^{2 x} + e^{3 x}

= \frac{4 e ^{x} ( - e ^{x} + 4 )}{64 + 48 e ^{x} + 12 e ^{2 x} + e ^{3 x}}

Expand

4 e^{x} (- e^{x} + 4) : - 4 e^{2 x} + 16 e^{x}

= \frac{- 4 e ^{2 x} + 16 e ^{x}}{64 + 48 e ^{x} + 12 e ^{2 x} + e ^{3 x}}

- \frac{s ^{2} + 6}{( s ^{2} + 12 ) ( s ^{2} + 2 )}

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

\frac{y ^{5} - 9 y ^{2} + 26 y - 24}{( y ^{2} - 4 y ) ( 1 - y ^{2} )}

(- 3 + 3 i 3)^{4}

2 k (1 + \frac{b}{4 x}) d x

What is expand (4e^x(-e^x+4))/((4+e^x)^3) ?
The solution to expand (4e^x(-e^x+4))/((4+e^x)^3) is (-4e^{2x}+16e^x)/(64+48e^x+12e^{2x)+e^{3x}}