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

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

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simplify e^{-1/x}(1+1/x)

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

1 \cdot (1 + \frac{1}{x}) = 1 + \frac{1}{x}

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

Join

1 + \frac{1}{x} : \frac{x + 1}{x}

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

Apply the fraction rule:

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

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

1.6 x 1 0^{- 19}

2.16 \cdot 1 0^{- 6}

2.89 \cdot 1 0^{- 11}

(1 + \frac{0.12}{60})^{- \frac{60}{30}} x^{75200}