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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

(sec (a) + tan (a)) (1 - sin (a))

\frac{( p - q ) ^{3}}{p + q}

sin (x) (sec (x) - csc (x))

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

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

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