Answer
False
Work Step by Step
In the given statement, common terms have been cancelled in addition, which is wrong. The correct solution is:
$$\begin{align*}
\dfrac{1}{x+3}+\dfrac{x+3}{2}&=\dfrac{2}{2(x+3)}+\dfrac{(x+3)^2}{2(x+3)}\\
&=\dfrac{2+(x+3)^2}{2(x+3)}\\
&=\dfrac{2+x^2+6x+9}{2(x+3)}\\
&=\dfrac{x^2+6x+11}{2(x+3)}.
\end{align*}$$
So the given statement is FALSE.
A true statement is:
$$\dfrac{1}{x+3}+\dfrac{3x+7}{2(x+3)}=\dfrac{3}{2}.$$
