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

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

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

expand

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

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

Solution steps

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

Expand

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

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

\frac{16 x}{( x ^{2} - 1 ) ^{2}}

\frac{2 3 + 2}{- 3}

\frac{- 2 t ^{5} - 2 t}{( t ^{4} - 1 ) ( t ^{2} - 1 )}

\frac{- b + 1}{( 2 - b ) ( - 2 + b )}

ln (x) (2 x^{2} + x) - x^{2} - x

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