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Popular >

simplify e^{ln(x)}*e^{-ln(x+1)}

Solution

simplify

e^{l n (x)} \cdot e^{- l n (x + 1)}

Solution

\frac{x}{x + 1}

Solution steps

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

Apply exponent rule:

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

e^{l n (x)} e^{- l n (x + 1)} = e^{l n (x) - l n (x + 1)}

= e^{l n (x) - l n (x + 1)}

Apply exponent rule:

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

= e^{l n (x)} e^{- l n (x + 1)}

Simplify

e^{l n (x)} : x

= x e^{- l n (x + 1)}

Simplify

e^{- l n (x + 1)} : (x + 1)^{- 1}

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

Simplify

= \frac{x}{x + 1}

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Frequently Asked Questions (FAQ)

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