(x^2)/(x^3)(x-2)

Answer 1

well, clearly you can cancel x^2 and you are left with

1 / x(x-2) = A/x + B/(x-2)

Now if you place the right side over the common denominator, you have

(A(x-2)+Bx)/(x(x-2))

In order for the two numerators to be identical, you need

(A+B)x-2A = 0x+1

That is,
A+B=0
-2A=1

A = -1/2
B = 1/2

1/x(x-2) = (-1/2)/x + (1/2)/(x-2)
or,
1/(2(x-2)) - 1/(2x)