Chapter 5, Systems of Equations and Inequalities - Section 5.3 - Partial Fractions - 5.3 Exercises - Page 462: 30

$\frac{x-4}{(2x-5)^2}=\frac{1}{2(x-5)}+\frac{-3}{2(2x-5)^2}$,

$\frac{x-4}{(2x-5)^2}=\frac{A}{2x-5}+\frac{B}{(2x-5)^2}$, $A(2x-5)+B=x-4$, $2A=1, A=\frac{1}{2}$, $-5A+B=-4, \frac{-5}{2}+B=-4, B=\frac{-3}{2}$. $\frac{x-4}{(2x-5)^2}=\frac{1}{2(x-5)}+\frac{-3}{2(2x-5)^2}$,