What is (e^x-e^{-x})(e^a-e^{-a})^{-1} ?

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

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simplify (e^x-e^{-x})(e^a-e^{-a})^{-1}

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

= \frac{e ^{x} - e ^{- x}}{e ^{a} - e ^{- a}}

Factor

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

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

Factor

e^{a} - e^{- a} : e^{- a} (e^{2 a} - 1)

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

Cancel

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

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

2^{- x} cos (x)

1.24 \times 1 0^{- 10}

(4.49 x 1 0^{10}) x (1.81 x 1 0^{10})

145.7 \cdot 1 0^{- 6}

360 e^{- 0.3 (10)}

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