I need help with this problem please!

Question

Suppose

f(x)=(7x-9)/(x^2-6x+9)

Then f(x)=A/(x-3)+B(x-3)^2

Where A= B=

Answer 1

(7x - 9) / (x - 3)² = A/(x - 3) + B/(x - 3)²

7x - 9 = A (x - 3) + B multiply all by (x - 3)²

7x - 9 = Ax - 3A + B

7x = Ax

7 = A

-3A + B = -9

-3(7) + B = -9

-21 + B = -9

B = 12