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

The solution to expand ((2-x)^3)/(3(x-1)^2) is (8-12x+6x^2-x^3)/(3x^2-6x+3)

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

expand

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

\frac{8 - 12 x + 6 x ^{2} - x ^{3}}{3 x ^{2} - 6 x + 3}

Solution steps

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

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

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

(2 - x)^{3} = 8 - 12 x + 6 x^{2} - x^{3}

= \frac{8 - 12 x + 6 x ^{2} - x ^{3}}{3 ( x ^{2} - 2 x + 1 )}

Expand

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

= \frac{8 - 12 x + 6 x ^{2} - x ^{3}}{3 x ^{2} - 6 x + 3}

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

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

(z - i)^{3}

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

(1 - e^{- x})^{2}

What is expand ((2-x)^3)/(3(x-1)^2) ?
The solution to expand ((2-x)^3)/(3(x-1)^2) is (8-12x+6x^2-x^3)/(3x^2-6x+3)