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I am interested in using the method of partial fractions to decompose a function of two variables. I have seen a few examples, but was interested in the specific rules. from the two examples on stack exchange there seems to be a necessity for complex expressions but I don't understand why or how they are actually used to decompose the fraction into two separate expressions.

Take for example the fraction,

$$f(x,y)=\frac{1}{(1-x)(1-y)}$$

can this be decomposed?

all of my attempts have led to an inconsistent systems, or an incomplete separation of my two variables (there is still a remainder or function that includes both the variables after the method is used). If this is a silly question I apologize in advance, but any insight would be fantastic.

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