Can someone please show that
is = -1/9/x + 2 - 1/3 / (x + 2)^2 + 1/9 / x - 1
1= A(x+2)(x-1)+ B(x-1)+ C(x+2)^2.
Now, letting x= -2 give B immediately. Letting x= 1 gives an equation involving both A and C but then letting x= 0 gives another equation in A and C and you can solve those two equations.