Determine the numerical values of the coefficients, A and B, where A B.
A=
B=
(x-6)(x+8)
how do you get the coefficients
See Wikipedia Method of undetermined coefficients
$\displaystyle \frac{2x-138}{(x-6)(x+8)} = \frac{A}{x-6} + \frac{B}{x+8}$
after getting a common denominator, the numerators form the equation ...
$\displaystyle 2x-138 = A(x+8) + B(x-6)$
let $\displaystyle x = 6$ ...
$\displaystyle A = -9$
let $\displaystyle x = -8$
$\displaystyle B = 11$