# partial fraction decomposition solve A,B and C

• Feb 6th 2008, 10:35 AM
waite3
partial fraction decomposition solve A,B and C
what is the value of A, B, and C of the partial fraction decomposition of this rational function.

(1x^2-1x+4)/((x+5)(x^2+9))= A/(x+5)+(Bx+C)/(x^2+9)

thanks
• Feb 6th 2008, 10:29 PM
CaptainBlack
Quote:

Originally Posted by waite3
what is the value of A, B, and C of the partial fraction decomposition of this rational function.

(1x^2-1x+4)/((x+5)(x^2+9))= A/(x+5)+(Bx+C)/(x^2+9)

thanks

You need to find $A,B$ and $C$ such that:

$A(x^2+9)+(Bx+C)(x+5) = x^2-x+4$

You do this by expanding the left hand side collecting the like powers of $x$ and then equating coefficients with those on the right hand side, so:

$A+B=1$
$5B+C=-1$
$9A+5C=4$

RonL