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} (1 + e^{2 x})

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

Cancel

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

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

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

e^{- \frac{1}{200}}

(5 x^{5} y^{2}) (5 x^{5} y^{7})

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