f(x)=(x-2)^2/(x+1)
f(x)'=[2(x-2)(x+1)-1*(x-2)^2]/(x+1)^2=(x-2)(x+4)/(x+1)^2
f(x)=(x^2+9)(x-3/x)
f(x)'=(x^2+9)(x-3/x)=f(x)=2x(x-3/x)+(x^2+9)(1+3/x^2)=3x^2+27/x^2+6