SOLUTION: Hello! I need help solving this equation. I have to Write the partial fraction decomposition of the rational expression. I used this sign" / " as a fraction sign so it is a fract

Algebra ->  Equations -> SOLUTION: Hello! I need help solving this equation. I have to Write the partial fraction decomposition of the rational expression. I used this sign" / " as a fraction sign so it is a fract      Log On


   

Question 977053: Hello!
I need help solving this equation. I have to Write the partial fraction decomposition of the rational expression.
I used this sign" / " as a fraction sign so it is a fraction
4x^2 – 15x – 27/x^3-9x
Please explain each step.
Thank you

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%284x%5E2-15x-27%29%2F%28x%5E3-9x%29=A%2Fx%2BB%2F%28x-3%29%2BC%2F%28x%2B3%29
4x%5E2-15x-27=A%28x-3%29%28x%2B3%29%2BBx%28x%2B3%29%2BCx%28x-3%29
4x%5E2-15x-27=A%28x%5E2-9%29%2BBx%5E2%2B3Bx%2BCx%5E2-3Cx
4x%5E2-15x-27=Ax%5E2-9A%2BBx%5E2%2B3Bx%2BCx%5E2-3Cx
4x%5E2-15x-27=%28A%2BB%2BC%29x%5E2%2B%283B-3C%29x-9A
Comparing,
1.A%2BB%2BC=4
2.3B-3C=-15
3.-9A=-27
So then,
A=3
Which then yields,
3%2BB%2BC=4
B%2BC=1
From eq. 2,
B-C=-5
Adding these two equations,
B%2BC%2BB-C=1-5
2B=-4
B=-2
And finally,
-2%2BC=1
C=3
So then,
%284x%5E2-15x-27%29%2F%28x%5E3-9x%29=3%2Fx-2%2F%28x-3%29%2B3%2F%28x%2B3%29