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

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

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expand (x+1+(x+1)e^{-2x})/x

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

\frac{x}{x} = 1

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

Cancel

\frac{e ^{- 2 x} x}{x} : e^{- 2 x}

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

\frac{- 50}{( s + 0.5 ) ( 0.2 s + 1 )}

\frac{1}{x ( K - x )}

(e^{t} + 1) h (t - 2)

(\frac{3 !}{2 ! 1 !}) (\frac{9}{16})^{1} (\frac{7}{16})^{2}

\frac{1}{s ( s + 100 ) ( s + 10 )}

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