Find the partial fraction decomposition 8x66x 32x 4 Choose

Find the partial fraction decomposition. 8x-66/(x - 3)^2(x + 4) Choose the correct pattern for the decomposition below, andill in any answer boxes to complete your choice./(x - 3) +/(x - 3)^2 +/(x + 4_/(x - 3)^2 + (x + 4)/(x - 3) +/(x - 3)^2 + x/(x + 4)/(x - 3) + x +/(x + 4)

Solution

option A) is correct answer

8x-66/(x-3)^2(x+4) = A/(x-3) +B/(x-3)^2 + C/(x+4)

8x-66/(x-3)^2(x+4) = [ A(x-3)(x+4) +B(x+4) +C(x-3)^2]/(x-3)^2(x+4)

8x-66 =  [ A(x-3)(x+4) +B(x+4) +C(x-3)^2]

8x-66 = x^2(A+C) +x(A+B-6C) -12A-4B+9C

now comparing

A+C=0 A=-C

A+B-6C=8

-12A-4B +9c =-66

After solving above equations we get A=2 ,C=-2 and B=-6

2,-6,-2