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

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

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expand ((x-6)-x^2(x-2)^2)/((x-2)^2)

expand

\frac{( x - 6 ) - x ^{2} ( x - 2 ) ^{2}}{( x - 2 ) ^{2}}

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

Solution steps

\frac{( x - 6 ) - x ^{2} ( x - 2 ) ^{2}}{( x - 2 ) ^{2}}

Remove parentheses:

(a) = a

= \frac{x - 6 - x ^{2} ( x - 2 ) ^{2}}{( x - 2 ) ^{2}}

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

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

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

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

Expand

x - 6 - x^{2} (x^{2} - 4 x + 4) : x - 6 - x^{4} + 4 x^{3} - 4 x^{2}

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

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

\frac{2 ( a - 1 + t )}{a - 1}

(3 x - 2 y = 1,) (4 x - y = 0,)

\frac{- 2 x - 9}{( x + 1 ) ^{2}}

\frac{x \cdot ( x - 1 )}{2}

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