What is expand (6x^3+14x^2+x-12)/(x(x-1)(x+2)^2) ?

The solution to expand (6x^3+14x^2+x-12)/(x(x-1)(x+2)^2) is (6x^3+14x^2+x-12)/(x^4+3x^3-4x)

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expand (6x^3+14x^2+x-12)/(x(x-1)(x+2)^2)

expand

\frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ( x - 1 ) ( x + 2 ) ^{2}}

\frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ^{4} + 3 x ^{3} - 4 x}

Solution steps

\frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ( x - 1 ) ( x + 2 ) ^{2}}

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

= \frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ( x - 1 ) ( x ^{2} + 4 x + 4 )}

Expand

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

= \frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ^{4} + 3 x ^{3} - 4 x}

\frac{1}{3} + \frac{2}{9} (1.1 - 1)

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

cos (x) (csc (x) - sec (x))

(\frac{x}{2} + \frac{1}{x})^{12}

\frac{x ^{9} + 5 x ^{5} - x ^{3} + 2021}{x ^{3} ( x ^{4} - 16 )}

What is expand (6x^3+14x^2+x-12)/(x(x-1)(x+2)^2) ?
The solution to expand (6x^3+14x^2+x-12)/(x(x-1)(x+2)^2) is (6x^3+14x^2+x-12)/(x^4+3x^3-4x)