Question

find the partial fraction decomposition: (4x+23)/(x^2-x-6)

Answer 1

youll have to factor the denominator

Answer 2

\[\frac{(4x+23)}{(x^2-x-6)}=\frac{(4x+23)}{(x+a)(x+b)}=\frac{A}{(x+a)}+\frac{B}{(x+b)}\]

Answer 3

then you solve for A and B as such:

\[4x+23=A(x+b)+B(x+a)\]
when x=-a we get
\[4(-a)+23=A(-a+b)+B(-a+a)\]
\[-4a+23=A(-a+b)\]
\[\frac{-4a+23}{-a+b}=A\]

Answer 4

same concept for solving for B; just make x=-b