What is expand (1+xe^{-5x})/(x(x+4)^2) ?

The solution to expand (1+xe^{-5x})/(x(x+4)^2) is (1+e^{-5x}x)/(x^3+8x^2+16x)

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expand (1+xe^{-5x})/(x(x+4)^2)

expand

\frac{1 + x e ^{- 5 x}}{x ( x + 4 ) ^{2}}

\frac{1 + e ^{- 5 x} x}{x ^{3} + 8 x ^{2} + 16 x}

Solution steps

\frac{1 + x e ^{- 5 x}}{x ( x + 4 ) ^{2}}

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

= \frac{1 + e ^{- 5 x} x}{x ( x ^{2} + 8 x + 16 )}

Expand

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

= \frac{1 + e ^{- 5 x} x}{x ^{3} + 8 x ^{2} + 16 x}

(4 - 4 x + x)^{2}

\frac{3 ( a + b ) ^{2}}{2}

(7 x^{\frac{5}{3}} + 49 x^{\frac{2}{3}}) (5)

(1 + 2 π \cdot sin (2 π x))^{2}

\frac{7}{( s ^{2} + 49 ) ( s ^{2} + 9 )}

What is expand (1+xe^{-5x})/(x(x+4)^2) ?
The solution to expand (1+xe^{-5x})/(x(x+4)^2) is (1+e^{-5x}x)/(x^3+8x^2+16x)