That is where I am at so far, and I just need a little help with finding the common denominator. Normally you would multiply A by the denominators of both B and C, but what about in this case? Since they are practically the same. Would I multiply A by or just by (x+2)?
Actually didn't understood what you actually meant.
Suppose
(x+1)/(x+2)(x+3)=[A/(x+2)] +B/x+3 or we may say
(x+1)/(x+2)(x+3)=[A(x+3)+B(x+2)]/(x+2)(x+3) or
x+1=A(x+3)+B(x+2)
if you put x=-2 you will get
-1=A(-2+3)+B(-2+2) or
-1=A
or A=-1
we take such value of x for which atleast 1 expression may become 0 so that calculating other constant may be calculated easily.
NOTE:actually same thing can be done by comparing LHS and RHS. But this substitution method is much easier.