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

The solution to expand (2-x)^3(1-1/x)^2 is -x^3+8x^2-13x+(8(x^2-2x+1)}{x^2}-\frac{12(x^2-2x+1))/x+6

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

expand

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

- x^{3} + 8 x^{2} - 13 x + \frac{8 ( x ^{2} - 2 x + 1 )}{x ^{2}} - \frac{12 ( x ^{2} - 2 x + 1 )}{x} + 6

Solution steps

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

Expand

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

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

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

Expand

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

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

Distribute parentheses

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

Simplify

\frac{x ^{2} - 2 x + 1}{x ^{2}} \cdot 8 + \frac{x ^{2} - 2 x + 1}{x ^{2}} (- 12 x) + \frac{x ^{2} - 2 x + 1}{x ^{2}} \cdot 6 x^{2} + \frac{x ^{2} - 2 x + 1}{x ^{2}} (- x^{3}) : - x^{3} + 8 x^{2} - 13 x + \frac{8 ( x ^{2} - 2 x + 1 )}{x ^{2}} - \frac{12 ( x ^{2} - 2 x + 1 )}{x} + 6

= - x^{3} + 8 x^{2} - 13 x + \frac{8 ( x ^{2} - 2 x + 1 )}{x ^{2}} - \frac{12 ( x ^{2} - 2 x + 1 )}{x} + 6

\frac{6 c ( a - 3 ) ( c + 4 )}{( a - 1 ) ( c + 5 )}

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

(\frac{d x}{y}) - (2 y - \frac{x}{y ^{2}}) d y

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

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

What is expand (2-x)^3(1-1/x)^2 ?
The solution to expand (2-x)^3(1-1/x)^2 is -x^3+8x^2-13x+(8(x^2-2x+1)}{x^2}-\frac{12(x^2-2x+1))/x+6