What is expand (2x+1)/((x+1)^3(x^2+4)^2) ?

The solution to expand (2x+1)/((x+1)^3(x^2+4)^2) is (2x+1)/(x^7+3x^6+11x^5+25x^4+40x^3+56x^2+48x+16)

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expand (2x+1)/((x+1)^3(x^2+4)^2)

expand

\frac{2 x + 1}{( x + 1 ) ^{3} ( x ^{2} + 4 ) ^{2}}

\frac{2 x + 1}{x ^{7} + 3 x ^{6} + 11 x ^{5} + 25 x ^{4} + 40 x ^{3} + 56 x ^{2} + 48 x + 16}

Solution steps

\frac{2 x + 1}{( x + 1 ) ^{3} ( x ^{2} + 4 ) ^{2}}

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

= \frac{2 x + 1}{( x ^{3} + 3 x ^{2} + 3 x + 1 ) ( x ^{2} + 4 ) ^{2}}

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

= \frac{2 x + 1}{( x ^{3} + 3 x ^{2} + 3 x + 1 ) ( x ^{4} + 8 x ^{2} + 16 )}

Expand

(x^{3} + 3 x^{2} + 3 x + 1) (x^{4} + 8 x^{2} + 16) : x^{7} + 3 x^{6} + 11 x^{5} + 25 x^{4} + 40 x^{3} + 56 x^{2} + 48 x + 16

= \frac{2 x + 1}{x ^{7} + 3 x ^{6} + 11 x ^{5} + 25 x ^{4} + 40 x ^{3} + 56 x ^{2} + 48 x + 16}

(x + \frac{1}{3}) (x - \frac{1}{3})

\frac{( 8 n ) !}{( 8 ( n + 1 ) ) !}

\frac{1}{9} (e^{3 x} \cdot 3 x - e^{3 x})

(- 2 + 2 i)^{5}

- \frac{1}{4} (6 e^{\frac{x}{2}} + e^{x})

What is expand (2x+1)/((x+1)^3(x^2+4)^2) ?
The solution to expand (2x+1)/((x+1)^3(x^2+4)^2) is (2x+1)/(x^7+3x^6+11x^5+25x^4+40x^3+56x^2+48x+16)