What is x/(1+x)*(1+x)e^{-x} ?

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

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

simplify

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

\frac{x}{e ^{x}}

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Cancel the common factor:

1 + x

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

Multiply:

x \cdot 1 = x

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

e^{- 0.0272}

13 (e^{- 9.3 \cdot 0.03636})

ln (2) \cdot 2^{- 3}

e^{- 3 t} cos (5 t)

0.49916 \cdot 1 0^{- 3}