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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply rule

- (- a) = a

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

e^{- x + x} = 1

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

Multiply:

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

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

x^{4} (x - 2)^{6} (x + 2)^{6}

t^{3} e^{(- 3 t)}

e^{- n} \cdot sin^{2} (e^{n})

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