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}}

(4 a) \cdot (3 a^{2})

(220 \cdot 1 0^{- 6}) \cdot (- 8 π sin (\frac{2 π t}{5}))

(((y)^{4})^{- 1})^{- 3}

(4 a^{2} b^{2}) \cdot (10 a^{3} b^{3} + 15 a^{2} b^{3})

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