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

The solution to expand ((e^x-e)^3)/(3e^x) is (e^{2x})/3-e^{x+1}+e^2-(e^{3-x})/3

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

expand

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

\frac{e ^{2 x}}{3} - e^{x + 1} + e^{2} - \frac{e ^{3 - x}}{3}

Solution steps

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

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

= \frac{e ^{3 x} - 3 e ^{2 x + 1} + 3 e ^{x + 2} - e ^{3}}{3 e ^{x}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{e ^{3 x} - 3 e ^{2 x + 1} + 3 e ^{x + 2} - e ^{3}}{3 e ^{x}} = \frac{e ^{3 x}}{3 e ^{x}} - \frac{3 e ^{2 x + 1}}{3 e ^{x}} + \frac{3 e ^{x + 2}}{3 e ^{x}} - \frac{e ^{3}}{3 e ^{x}}

= \frac{e ^{3 x}}{3 e ^{x}} - \frac{3 e ^{2 x + 1}}{3 e ^{x}} + \frac{3 e ^{x + 2}}{3 e ^{x}} - \frac{e ^{3}}{3 e ^{x}}

\frac{e ^{3 x}}{3 e ^{x}} = \frac{e ^{2 x}}{3}

\frac{3 e ^{2 x + 1}}{3 e ^{x}} = e^{x + 1}

\frac{3 e ^{x + 2}}{3 e ^{x}} = e^{2}

\frac{e ^{3}}{3 e ^{x}} = \frac{e ^{3 - x}}{3}

= \frac{e ^{2 x}}{3} - e^{x + 1} + e^{2} - \frac{e ^{- x + 3}}{3}

(x + 4) ln (3 x + 5)

\frac{0.9}{s ( s ^{2} + 2.8 s + 1 )}

1 0^{(\frac{1}{x - 1})}

\frac{( x ^{2} + 1 ) \cdot x ^{2} - 1}{3 x + 2}

\frac{24}{4 - y} (y)

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