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

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

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

simplify

e^{- x} (\frac{e ^{x} - e ^{- x}}{2})

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

Solution steps

e^{- x} (\frac{e ^{x} - e ^{- x}}{2})

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

Cancel

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

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

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

(3.7 x 1 0^{7}) (8 x 1 0^{4})

6.83089 \cdot 1 0^{- 15}

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(4 x^{2} y) (3 x^{3} y^{2})

7 e^{- 93 (20)}

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