To break into partial fractions, the numerator must have a smaller degree
than the denominator.  If the numerator has the same or larger degree, we
must first divide by long division:

                      1
x² + x - 6)x² + 9x +  8 
           x² +  x -  6
                8x + 14

 
 = 1 + 

So we break  into partial fractions and add 
what we get to the 1 above:

 = 

 =  + 

 8x + 14 = A(x - 2) + B(x + 3)

This must be an identity for all x, so we substitute 2 for x to make the
first term on the right become 0:

 8(2) + 14 = A(2 - 2) + B(2 + 3)
   16 + 14 = 5B
        30 = 5B
         6 = B 

Substitute -3 for x to make the second term on the right become 0:

 8(-3) + 14 = A(-3 - 2) + B(-3 + 3)
   -24 + 14 = -5A
        -10 = -5A
          2 = A

 =  + 



Now we add that to 1 and get

 = 1 +  + 

Edwin