f(x)=x/(2-3x) and f(x+h)=(x+h)/(2-3(x+h))=(x+h)/(2-3x-3h).
The change in f is (x+h)/(2-3x-3h)-x/(2-3x)=
((x+h)(2-3x)-x(2-3x-3h))/((2-3x-3h)(2-3x))=
(x(2-3x)+h(2-3x)-x(2-3x)+3hx)/((2-3x)²-3h(2-3x))=
(2h)/(4-12x+9x²-6h+9hx).
The change in x is just h. The rate of change is (change in f)/(change in x)=
((2h)/(4-12x+9x²-6h+9hx))/h=2/(4-12x+9x²-6h+9hx)=2/((2-3x)²-6h+9hx).
Put x=2: rate of change: 2/(2-6)²=2/(-4)²=2/16=⅛. This is the instantaneous rate of change as h→0.