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

Factor

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

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

Refine

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

6 x^{3} \cdot 10 x

11 x^{2 - 78 x + 7}

0.25 x^{2} - x + 1

(- 2 x^{9} y^{4}) - 4

1 - 6 4^{2}

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^x+1)(e^x-1)