What is factor e^{x-y}-e^{y-x} ?

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

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

factor

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply exponent rule:

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

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

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

Factor out common term

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

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

Refine

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

(lo g_{10} (tan (x)))^{2}

(11 x + 1) - 12

- (x)^{4} + 8 (x)^{2} - 5

A - B

g (0.4)

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