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.