question/algebra

Question

Find constants A,B and C such that

(3x²-12x+11)/[(x-1)(x-2)(x-3)]

=(A/x-1)+(B/x-2)+(C/x-3)

Answer 1

A/(x-1) + B/(x-2) + C/(x-3) =

 

 [A(x-2)(x-3) + B(x-1)(x-3) + C(x-1)(x-2)] / [(x-1)(x-2)(x-3)]

 

So, A(x-2)(x-3) + B(x-1)(x-3) + C(x-1)(x-2) = 3x² - 12x + 11

 

   If x = 1, then 6A = 2.  So, A = 1/3

 

   If x = 2, then -B = -1.  So, B = 1

 

   If x = 3, then 2C = 2.  So, C = 1