Add, subtract, multiply, divide

Algebra Level pending

For some nonzero reals \(a,b\), the numbers \(a+b, a-b, ab, \frac{a}{b}\) form an arithmetical progression in that order. If \(a+b\) can be expressed as \(\frac{x}{y}\) where \(x\) is an integer, \(y\) is a positive integer, and \(x,y\) are coprime, determine the value of \(|x+y|\).