Answer
$\frac{1}{2x+3}-\frac{3}{(2x+3)^2}$
Work Step by Step
Step 1. Factor the denominator as $(2x+3)^2$
Step 2. Assume the end results as $\frac{A}{2x+3}+\frac{B}{(2x+3)^2}$
Step 3. Combine the above functions as:
$\frac{A(2x+3)+B}{(2x+3)^2}=\frac{2Ax+3A+B}{(2x+3)^2}$
Step 4. Compare the above result with the original expression to set up the following system of equations:
\begin{cases} 2A=2 \\ 3A+B=0 \end{cases}
Step 5. Use substitution to solve the above equations and get $A=1, B=-3$
Step 6. Write the final results as:
$\frac{1}{2x+3}-\frac{3}{(2x+3)^2}$
