What is factor ye^{x-y}+ye^{-x-y} ?

The solution to factor ye^{x-y}+ye^{-x-y} is e^{-x-y}y(e^{2x}+1)

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factor ye^{x-y}+ye^{-x-y}

factor

y e^{x - y} + y e^{- x - y}

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

Solution steps

y e^{x - y} + y e^{- x - y}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= e^{x} e^{- y} y + e^{- x} e^{- y} y

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

e^{x} = e^{- x} e^{2 x}

= y e^{- x} e^{2 x} e^{- y} + y e^{- x} e^{- y}

Factor out common term

y e^{- x} e^{- y}

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

Refine

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

\frac{e ^{8} - 1}{40}

cos (180 - 2 a)

x y - x z + 3 y - 3 z

(x - 5) + (4 x^{2})

9 b^{2 x} - \frac{1}{4}

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