Derivative of polynomial division in Maple

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This is proably a beginner's question about Maple. I'm trying to use Maple to differentiate:

$$\frac{(z^2-1)^2}{(az-1)(z-a)}$$

Where $a$ is a constant.

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  • On the first line, is there a way to tell Maple not to expand the denominator?
  • How can you tell Maple that $z$ is variable and $a$ is constant?
  • On the second line, what does Maple mean with $D(az)$ ?
  • The differential seems to be missing the term with $(z^2-1)^2 (az-1)$ in the numerator?

Any hints or pointers welcome.

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You need to type out $a*z$ instead of $az$. Maple thinks, $az$ is another variable. Also $$(z^2 - 1)^2/((a*z-1)*(z-a))$$ Will give the desired output. This pretty much fixes anything.