a/(b-1)-(a+1)/(b+1)
=a(b+1)/(b+1)(b-1)-(a+1)(b-1)/(b+1)(b-1)
=(ab+a)/(b²-1)-(ab+b-a-1)/(b²-1)
=(ab+a-ab-b+a+1)/(b²-1)
=(2a-b+1)/(b²-1)