What is expand (e^{-2x})/((x-1)(x+4)^2) ?

The solution to expand (e^{-2x})/((x-1)(x+4)^2) is (e^{-2x})/(x^3+7x^2+8x-16)

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expand (e^{-2x})/((x-1)(x+4)^2)

expand

\frac{e ^{- 2 x}}{( x - 1 ) ( x + 4 ) ^{2}}

\frac{e ^{- 2 x}}{x ^{3} + 7 x ^{2} + 8 x - 16}

Solution steps

\frac{e ^{- 2 x}}{( x - 1 ) ( x + 4 ) ^{2}}

(x + 4)^{2} = x^{2} + 8 x + 16

= \frac{e ^{- 2 x}}{( x - 1 ) ( x ^{2} + 8 x + 16 )}

Expand

(x - 1) (x^{2} + 8 x + 16) : x^{3} + 7 x^{2} + 8 x - 16

= \frac{e ^{- 2 x}}{x ^{3} + 7 x ^{2} + 8 x - 16}

\frac{x ^{2} ( 8 - x ) ^{3}}{24}

\frac{d x}{( x + 5 ) ( x + 2 )}

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

\frac{4 ( x + h ) - 5 - ( 4 ( x ) - 5 )}{h}

\frac{180 ( x - 2 )}{x}

What is expand (e^{-2x})/((x-1)(x+4)^2) ?
The solution to expand (e^{-2x})/((x-1)(x+4)^2) is (e^{-2x})/(x^3+7x^2+8x-16)