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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

Factor

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

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

Cancel

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

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

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e^{- j wt} \cdot e^{4 j wt}

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