[(a-b)/(a+b)-(a+b)/(a-b)]/b/(a+b)+b/(a-b)
={[(a-b)²-(a+b)²]/(a²-b²)}/{[(a-b)²+(a+b)²]/(a²-b²)}
=-4ab/(2a²+2b²)
=-2ab/(a²+b²)