Write the partial fraction decomposition of the rational expression. Check your result algebraically.
(x2 – 7x + 16)/[(x + 2)(x2 – 4x + 5)]
The Attempt at a Solution
[A/(x+2)] + [(Bx+C)/(x2-4x+5)]
A+B=1 => B=1-A
-4A+B+C=-7 => Will need to plugin later
5A+C=16 => C=16-5A
-4A+B+C=-7 => 4A+1-A+16-5A= -10A=17 A=(-17/10)
Now I plug A back into the others
B=1-(-17/10) => B=(27/10)
C=16-5(-17/10) => C= (49/2)
Result: [(-17/10)/(x+2)] + [((27x/10)+(49/2))/(x2-4x+5)]
However, I am being told the answer is wrong. What is it that I am doing wrong?