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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

e^{- t} \cdot 2 e^{t}

e^{- 3 l n ∣ 1 + x ∣}

e^{- 1.6} \cdot 60

2 \cdot \frac{e ^{2}}{x ^{2}}

6.66 \cdot 1 0^{- 8}

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