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

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

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

expand

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

\frac{2 - 6 x - 3 x ^{2}}{4 x ^{3} - 3 x + 1}

Solution steps

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

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

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

Expand

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

= \frac{2 - 6 x - 3 x ^{2}}{4 x ^{3} - 3 x + 1}

\frac{3}{4} (e^{- 2 t} - e^{- 10 t})

(2 + e^{- 2 t})^{2}

(x - x)^{3}

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

(4 x^{3} y^{3} - 2 x y) d x + (3 x^{4} y^{2} - x^{2}) d y

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