Expand a function into a series (approximation without ever knowing the unknowns)

36 Views Asked by At

I am having the following problem: We have the unknowns x and y for which we know the following: x/(x+y) = k where k is a real known number. We also have some known variables a and b which are real numbers and each one of them is less than x and y. Is there a possible way to expand the following expression into a series or a mathematical approximation with x and y separated from a and b?

(x+a)/(x+y+a+b)

For example something like: k/(a+b)+2*k/(a+b)+... In other words, would it be possible to know an approximate result of this expression without ever knowing x and y?