What is e^{-x}(e^xx-e^x) ?

The solution to e^{-x}(e^xx-e^x) is x-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify e^{-x}(e^xx-e^x)

simplify

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

x - 1

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

1 \cdot (e^{x} x - e^{x}) = e^{x} x - e^{x}

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

Factor out common term

e^{x}

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

Cancel the common factor:

e^{x}

= x - 1

x^{2} cos (h) (3 x)

\frac{( n + 1 ) ! ^{k}}{( n ! ) ^{k}}

1.5 m x m x^{10} m