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

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

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

simplify

(e^{x} + e^{- x}) e^{- x}

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

Solution steps

(e^{x} + e^{- x}) e^{- x}

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

Factor

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

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

Cancel

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

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

(x^{3} y^{3}) (y^{4} z^{5})

41 \cdot 1 0^{- 7} \cdot 6750 \cdot 15 \cdot \frac{1 \cdot ( 6 \cdot 1 0 ^{- 4} )}{0.5}

2 x 4 x - 1

e^{x} \cdot 1^{- 1}

159150 \cdot \frac{1}{2} \cdot (34.62 - 13.91 - 0.977)^{2} \cdot 1 0^{- 6}

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