Step 1 :Given the expression \(\left(\frac{3}{2 t+1}-\frac{t}{2 t^{2}+5 t+2}\right)(t+2)\), we are asked to simplify it.
Step 2 :First, distribute the term \((t+2)\) to both terms in the parentheses. This gives us \(\frac{3(t+2)}{2 t+1}-\frac{t(t+2)}{2 t^{2}+5 t+2}\).
Step 3 :Simplify the resulting expression by combining like terms and simplifying the fractions if possible.
Step 4 :After simplifying, we get \(\frac{2(t + 3)}{2t + 1}\).
Step 5 :Final Answer: The simplified expression is \(\boxed{\frac{2 t+6}{2 t+1}}\). Therefore, the correct option is (d).