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

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

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

expand

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

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

Solution steps

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

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

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

Expand

z^{2} (z^{2} - 1) : z^{4} - z^{2}

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

2 w (13 w + \frac{168}{w ^{2}})

\frac{4}{x ( x ^{2} + 5 )}

(2 x - y + 1) d x + (4 x - 2 y + 3) d y

(s + 1.47) (\frac{0.5}{s + 1.47} + 1.7)

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