What is expand z/((z-0.5)(z-1)^2) ?

The solution to expand z/((z-0.5)(z-1)^2) is z/(z^3-2.5z^2+2z-0.5)

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expand z/((z-0.5)(z-1)^2)

expand

\frac{z}{( z - 0.5 ) ( z - 1 ) ^{2}}

\frac{z}{z ^{3} - 2.5 z ^{2} + 2 z - 0.5}

Solution steps

\frac{z}{( z - 0.5 ) ( z - 1 ) ^{2}}

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

= \frac{z}{( z - 0.5 ) ( z ^{2} - 2 z + 1 )}

Expand

(z - 0.5) (z^{2} - 2 z + 1) : z^{3} - 2.5 z^{2} + 2 z - 0.5

= \frac{z}{z ^{3} - 2.5 z ^{2} + 2 z - 0.5}

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

\frac{f ( f - a - b + ab )}{f - a}

6 (3 x - 1) e^{2 x + 1}

b (2 a - b - 4 = 0)

e^{(t - 1) 2}

What is expand z/((z-0.5)(z-1)^2) ?
The solution to expand z/((z-0.5)(z-1)^2) is z/(z^3-2.5z^2+2z-0.5)