What is expand (2e^x(-e^x+2))/((e^x+2)^3) ?

The solution to expand (2e^x(-e^x+2))/((e^x+2)^3) is (-2e^{2x}+4e^x)/(e^{3x)+6e^{2x}+12e^x+8}

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expand (2e^x(-e^x+2))/((e^x+2)^3)

expand

\frac{2 e ^{x} ( - e ^{x} + 2 )}{( e ^{x} + 2 ) ^{3}}

\frac{- 2 e ^{2 x} + 4 e ^{x}}{e ^{3 x} + 6 e ^{2 x} + 12 e ^{x} + 8}

Solution steps

\frac{2 e ^{x} ( - e ^{x} + 2 )}{( e ^{x} + 2 ) ^{3}}

(e^{x} + 2)^{3} = e^{3 x} + 6 e^{2 x} + 12 e^{x} + 8

= \frac{2 e ^{x} ( - e ^{x} + 2 )}{e ^{3 x} + 6 e ^{2 x} + 12 e ^{x} + 8}

Expand

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

= \frac{- 2 e ^{2 x} + 4 e ^{x}}{e ^{3 x} + 6 e ^{2 x} + 12 e ^{x} + 8}

8 x 2 - 24 x y + 6 y 2

(x - \frac{1}{3}) (x - \frac{2}{3})

\frac{( - 9 x ^{2} + 13 ) ^{2}}{81}

(e - 2, e + 1) \cdot (x, y)

\frac{\frac{d ^{2}}{d x ^{2}} ( 3 x ^{2} )}{( x ^{2} - 25 ) ^{2}}

What is expand (2e^x(-e^x+2))/((e^x+2)^3) ?
The solution to expand (2e^x(-e^x+2))/((e^x+2)^3) is (-2e^{2x}+4e^x)/(e^{3x)+6e^{2x}+12e^x+8}