Remember, for partial fractions when given a ratonal functon of the form f(x)/x^2 you put it in partial fractions in the form A/x + B/x^2, similarly

......x..........=.......A......+........B

----------.......---------.....--------

(x - 2)^2.........(x - 2)........(x - 2)^2

now we multiply through by (x - 2)^2. we obtain:

x = A(x - 2) + B

=> x = Ax + (B - 2A)

now we equate the coefficients of like powers of x

=> 1 = A

=> 0 = B - 2A

=> 0 = B - 2

=> B = 2

so

......x..........=.......1......+........2

----------.......---------.....--------

(x - 2)^2.........(x - 2)........(x - 2)^2