Simplify the expression, if possible.
\[
\left(\frac{3}{2 t+1}-\frac{t}{2 t^{2}+5 t+2}\right)(t+2)
\]
Select one:
a. $\frac{2 t+6}{(2 t+1)(t+2)}$
b. $\frac{3 t+6}{t+2}$
C. $\frac{3 t+6}{2 t+1}$
d. $\frac{2 t+6}{2 t+1}$
Answer
Final Answer: The simplified expression is \(\boxed{\frac{2 t+6}{2 t+1}}\). Therefore, the correct option is (d).
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).
