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

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

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

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

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

= - \frac{z ( z + 2 )}{z ^{4} + 2 z ^{3} + 3 z ^{2} + 2 z + 1}

Expand

z (z + 2) : z^{2} + 2 z

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

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

\frac{x + 4}{( x - 2 ) ( x - 4 )}

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

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

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