What is expand (2δx+δ)/(x(x+1)^3) ?

The solution to expand (2δx+δ)/(x(x+1)^3) is (2δx+δ)/(x^4+3x^3+3x^2+x)

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expand (2δx+δ)/(x(x+1)^3)

expand

\frac{2 δ x + δ}{x ( x + 1 ) ^{3}}

\frac{2 δ x + δ}{x ^{4} + 3 x ^{3} + 3 x ^{2} + x}

Solution steps

\frac{2 δ x + δ}{x ( x + 1 ) ^{3}}

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

= \frac{2 δ x + δ}{x ( x ^{3} + 3 x ^{2} + 3 x + 1 )}

Expand

x (x^{3} + 3 x^{2} + 3 x + 1) : x^{4} + 3 x^{3} + 3 x^{2} + x

= \frac{2 δ x + δ}{x ^{4} + 3 x ^{3} + 3 x ^{2} + x}

\frac{d}{d x} ((2 x - 8 c) (9 - x^{2})^{2}) - 2

\frac{2}{( 1 - 2 x ) ^{2}}

\frac{d}{d x} ((f (x)) (2 x^{3} - 15 x^{2} + 24 x + 19))

(x + 2)^{3} - e^{3 x}

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

What is expand (2δx+δ)/(x(x+1)^3) ?
The solution to expand (2δx+δ)/(x(x+1)^3) is (2δx+δ)/(x^4+3x^3+3x^2+x)