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Popular >

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

Solution

simplify

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

Solution

\frac{e ^{x}}{e ^{x} + 1}

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

= \frac{1 \cdot e ^{x}}{1 + e ^{x}}

Multiply:

1 \cdot e^{x} = e^{x}

= \frac{e ^{x}}{1 + e ^{x}}

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Frequently Asked Questions (FAQ)

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