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

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

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

expand

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

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

Solution steps

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

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

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

(x - 2 + 3) (x - 2 - 3)

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

\frac{k ^{2} ( k + 1 ) ^{2}}{4}

(x + 3 - 2) (x + 3 + 2)

(x - 1 - 2) (x - 1 + 2)

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