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## Homework Statement

Write the partial fraction decomposition of the rational expression. Check your result algebraically.

(x

^{2}– 7x + 16)/[(x + 2)(x2 – 4x + 5)]

## The Attempt at a Solution

[A/(x+2)] + [(Bx+C)/(x

^{2}-4x+5)]

x

^{2}-7x+16= A(X

^{2}-4x+5)+(Bx+C)(x+2)

X

^{2}-7x+16=[A+B]x

^{2}+[-4A+B+C]x+[5A+C]

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))/(x

^{2}-4x+5)]

However, I am being told the answer is wrong. What is it that I am doing wrong?