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,


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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