Answer
$\frac{1}{2(2x-5)}-\frac{3}{2(2x-5)^2}$
Work Step by Step
Step 1. As the denominator is already factorized, assume the end results as: $\frac{A}{2x-5}+\frac{B}{(2x-5)^2}$
Step 2. Combine the above functions as:
$\frac{A(2x-5)+B}{(2x-5)^2}=\frac{2Ax-5A+B}{(2x+3)^2}$
Step 3. Compare the above result with the original expression to set up the following system of equations:
\begin{cases} 2A=1 \\ -5A+B=-4 \end{cases}
Step 4. Use substitution to solve the above equations and get $A=\frac{1}{2}, B=-\frac{3}{2}$
Step 5. Write the final results as:
$\frac{1}{2(2x-5)}-\frac{3}{2(2x-5)^2}$
