What is expand-z d/(dz)((az(z+a))/((z-a)^3)) ?

The solution to expand-z d/(dz)((az(z+a))/((z-a)^3)) is -z d/(dz)((az^2+a^2z)/((z-a)^3))

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expand-z d/(dz)((az(z+a))/((z-a)^3))

expand

- z \frac{d}{d z} (\frac{a z ( z + a )}{( z - a ) ^{3}})

- z \frac{d}{d z} (\frac{a z ^{2} + a ^{2} z}{( z - a ) ^{3}})

Solution steps

- z \frac{d}{d z} (\frac{a z ( z + a )}{( z - a ) ^{3}})

Expand

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

= - z \frac{d}{d z} (\frac{a z ^{2} + a ^{2} z}{( z - a ) ^{3}})

\frac{( x - 1 )}{2 \cdot ( x - 3 ) ^{2}}

\frac{13 ( s + 2 ) ( s + 1 )}{s ^{3} + 9 s ^{2} + 138 s + 260}

d x (3 x - \frac{2}{x} + 1)

3 cos (t) sin (t) - (2 t - 5)^{2} sin (t) + 3

\frac{3}{8} (2 x^{2} sin (2 x) + 2 x cos (2 x) - sin (2 x))

What is expand-z d/(dz)((az(z+a))/((z-a)^3)) ?
The solution to expand-z d/(dz)((az(z+a))/((z-a)^3)) is -z d/(dz)((az^2+a^2z)/((z-a)^3))