SOLUTION: Find the constants A, B, and C for: (3x+4)/((x-1)^2 * (x+2)) = A/(x-1) + B/(x-1)^2 + C/(x+2)

Algebra ->  Equations -> SOLUTION: Find the constants A, B, and C for: (3x+4)/((x-1)^2 * (x+2)) = A/(x-1) + B/(x-1)^2 + C/(x+2)       Log On


   

Question 1040834: Find the constants A, B, and C for:
(3x+4)/((x-1)^2 * (x+2)) = A/(x-1) + B/(x-1)^2 + C/(x+2)

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply left and right by simplest common denominator.

3x%2B4=A%28x-1%29%28x%2B2%29%2BB%28x%2B2%29%2BC%28x-1%29%5E2

Simplify right side.

3x%2B4=Ax%5E2-Ax-2A%2BBx%2B2B%2BCx%5E2-2Cx%2BC

Form the right side into simplified decreasing powers of x.

3x%2B4=%28A%2BB%29x%5E2%28B-A-2C%29x%2B%282B-A%2BC%29

Compare the corresponding parts or coefficients to write the system of equations.

system%28A%2BB=0%2CB-A-2C=3%2C2B-A%2BC=4%29
Finish! Solve the system.