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

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

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

expand

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

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

Solution steps

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

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

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

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

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

(y^{2} + t y^{2}) y^{'} (t) + t^{2} - y t^{2}

(8 e^{2} b^{5} - 10)^{2}

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

\frac{\partial}{\partial y} ((z) (x e^{yz} + y e^{x z} + 3 x yz - 2))

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

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