What is expand (20(25e^{-x/(25)}x-250e^{-x/(25)}))/x ?

The solution to expand (20(25e^{-x/(25)}x-250e^{-x/(25)}))/x is 500e^{-x/(25)}-(5000e^{-x/(25)})/x

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expand (20(25e^{-x/(25)}x-250e^{-x/(25)}))/x

expand

\frac{20 ( 25 e ^{- \frac{x}{25}} x - 250 e ^{- \frac{x}{25}} )}{x}

500 e^{- \frac{x}{25}} - \frac{5000 e ^{- \frac{x}{25}}}{x}

Solution steps

\frac{20 ( 25 e ^{- \frac{x}{25}} x - 250 e ^{- \frac{x}{25}} )}{x}

Expand

20 (25 e^{- \frac{x}{25}} x - 250 e^{- \frac{x}{25}}) : 500 e^{- \frac{x}{25}} x - 5000 e^{- \frac{x}{25}}

= \frac{500 e ^{- \frac{x}{25}} x - 5000 e ^{- \frac{x}{25}}}{x}

Apply the fraction rule:

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

\frac{500 e ^{- \frac{x}{25}} x - 5000 e ^{- \frac{x}{25}}}{x} = \frac{500 e ^{- \frac{x}{25}} x}{x} - \frac{5000 e ^{- \frac{x}{25}}}{x}

= \frac{500 e ^{- \frac{x}{25}} x}{x} - \frac{5000 e ^{- \frac{x}{25}}}{x}

Cancel

\frac{500 e ^{- \frac{x}{25}} x}{x} : 500 e^{- \frac{x}{25}}

= 500 e^{- \frac{x}{25}} - \frac{5000 e ^{- \frac{x}{25}}}{x}

\frac{π ( 32 2 - 40 )}{15}

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\frac{6}{( x - 6 ) ( x + 1 )}

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(x^{2} + y^{2} + 1) d x - (x y + y) d y

What is expand (20(25e^{-x/(25)}x-250e^{-x/(25)}))/x ?
The solution to expand (20(25e^{-x/(25)}x-250e^{-x/(25)}))/x is 500e^{-x/(25)}-(5000e^{-x/(25)})/x