# Partial fractions - alternative result

I have the following fraction:

$$\frac{z}{(z-1)(z-2)}$$

When I try to decompose it to partial fractions, I get:

$$-\frac{1}{z-1} + \frac{2}{z-2}$$

But the result in my book is:

$$-\frac{z}{z-1} + \frac{z}{z-2}$$

Both results are correct, but, how am I supposed to get the second one?

• The book's result is non-standard, because one tries to get the degree of the numerator less than the degree of the denominator. – almagest May 16 '16 at 16:57
• I need it in the second form to perform the inverse Z-transform on it later. – Eenoku May 16 '16 at 16:59

$\frac{z}{(z-1)(z-2)}=\frac{z(z-1)-z(z-2)}{(z-1)(z-2)}=...$