ADVANCED EXERCISES

Decompose each fraction into partial fractions:

(2)     5x2 + 3x + 6
       ---------------
        x3 + 2x2 + 3x

Let    5x2 + 3x + 6       A      Bx + C
      --------------  =  -- + ------------
       x3 + 2x2 + 3x      x    x2 + 2x + 3

Then we get:

	5x2 + 3x + 6 = A(x2 + 2x + 3) + (Bx + C)x
                                = Ax2 2Ax + 3A + Bx2 + Cx
                                = (A + B)x2 + (2A + C)x + 3A

         3A = 6  ==>  A = 2
     2A + C = 3  ==>  2(2) + C = 3  ==>  C = -1
      A + B = 5  ==>  2 + B = 5  ==>  B = 3

Therefore the solution is:

       5x2 + 3x + 6       2      3x - 1
      --------------  =  -- + ------------
       x3 + 2x2 + 3x      x    x2 + 2x + 3