Partial Fraction Decomposition—Multiple Variables

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What's the best approach to solving the partial-fraction decomposition of the following expression?

$$\frac{1}{(a-y)(b-y)}$$

The expression is not of the following forms:

But I know the solution is

$$= \frac{1}{(a-b)(y-a)}-\frac{1}{(a-b)(y-b)}$$

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I don't use such tables. Any time I want to do a partial fraction decomposition, I just write (e.g.) $\frac{1}{(a-y)(b-y)}=\frac{A}{a-y}+\frac{B}{b-y}$ and then determine A and B.