Write the follwing into partial fraction. (2x-5)/(x^2-7x-8)

We need to rewrite into partial
fractions.

First we will factor the
denominator.

==> x^2 - 7x -8 =
(x-8)(x+1)

==> (2x-5)/x^2 -7x -8 = A/(x-8) +
B(x+1)

Now we will multiply by
(x-8)(x+1)

==> 2x -5 = A(x+1) +
B(x-8)

==> 2x -5 = Ax + A + Bx -
8B

==> 2x-5 = (A+B)x +
(A-8B)

==> A+B = 2 ==> A =
2-B

A-8B = -5

==> (2-B)
- 8B = -5

==> -9B =
-7

==> B =
7/9

==> A = 2- 7/9 =
11/9

==> (2x-5)/x^2-7x-8 = 11/9(x-8) +
7/9(x+1)