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Popular >

simplify (e^{-a/x})/(e^{-b/x)}

Solution

simplify

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply rule

- (- a) = a

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

Join

- \frac{a}{x} + \frac{b}{x} : \frac{- a + b}{x}

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

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

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Frequently Asked Questions (FAQ)

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