Write the partial fraction decomposition of .

Multiply each side of the equation by (x+8)(x-3) [the least common denominator]

x-25=A(x-3)+B(x+8)

This equation is true for all x so we can substitute any number for x.

Let’s choose x=3 and x=-8 for convenience.

When x=3

3-25=A(3-3)+B(3+8)=-22=11B

B=-2

When x=-8

-8-25=A(-8-3)+B(-8+8)=-33=-11A

A=3

So, the partial fraction decomposition is: