What is expand (x^3+3x^2+6x+6)/((x^2+x+1)^2) ?

The solution to expand (x^3+3x^2+6x+6)/((x^2+x+1)^2) is (x^3+3x^2+6x+6)/(x^4+2x^3+3x^2+2x+1)

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expand (x^3+3x^2+6x+6)/((x^2+x+1)^2)

expand

\frac{x ^{3} + 3 x ^{2} + 6 x + 6}{( x ^{2} + x + 1 ) ^{2}}

\frac{x ^{3} + 3 x ^{2} + 6 x + 6}{x ^{4} + 2 x ^{3} + 3 x ^{2} + 2 x + 1}

Solution steps

\frac{x ^{3} + 3 x ^{2} + 6 x + 6}{( x ^{2} + x + 1 ) ^{2}}

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

= \frac{x ^{3} + 3 x ^{2} + 6 x + 6}{x ^{4} + 2 x ^{3} + 3 x ^{2} + 2 x + 1}

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

(x + 2 y)^{2}

\frac{s}{( s - 1 ) ( s + 1 )}

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

\frac{L - 11}{( s + 1 ) ( s ^{2} + 1 )}

What is expand (x^3+3x^2+6x+6)/((x^2+x+1)^2) ?
The solution to expand (x^3+3x^2+6x+6)/((x^2+x+1)^2) is (x^3+3x^2+6x+6)/(x^4+2x^3+3x^2+2x+1)