What is 1/x e^{-x}*(xe^x-e^x) ?

The solution to 1/x e^{-x}*(xe^x-e^x) is (x-1)/x

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simplify 1/x e^{-x}*(xe^x-e^x)

simplify

\frac{1}{x} e^{- x} \cdot (x e^{x} - e^{x})

\frac{x - 1}{x}

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{x} \cdot \frac{1}{e ^{x}} (e^{x} x - e^{x})

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 1 \cdot ( x e ^{x} - e ^{x} )}{x e ^{x}}

1 \cdot 1 \cdot (x e^{x} - e^{x}) = e^{x} x - e^{x}

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

Factor out common term

e^{x}

= \frac{e ^{x} ( x - 1 )}{x e ^{x}}

Cancel the common factor:

e^{x}

= \frac{x - 1}{x}

[{(2^{- 1})^{- 1}}^{- 1}]^{- 1}

10.5 \cdot 1 0^{- 3}

x d x

- 2^{- t} ln (2) (cos (2 π t))

2.7 \cdot 1 0^{- 6}

What is 1/x e^{-x}*(xe^x-e^x) ?
The solution to 1/x e^{-x}*(xe^x-e^x) is (x-1)/x