4. Let three different lines be:
$$
\begin{array}{l}
l_{1}: a x+2 b y+3(a+b+1)=0, \\
l_{2}: b x+2(a+b+1) y+3 a=0, \\
l_{3}:(a+b+1) x+2 a y+3 b=0,
\end{array}
$$

Then the necessary and sufficient condition for them to intersect at one point is $\qquad$
The necessary and sufficient condition for $l_{1}, l_{2}, l_{3}$ to intersect at one point is 
\[
\left|\begin{array}{ccc}
a & 2 b & 3(a+b+1) \\
b & 2(a+b+1) & 3 a \\
a+b+1 & 2 a & 3 b
\end{array}\right|=0
\]
\[
\begin{array}{l}
\Rightarrow\left|\begin{array}{ccc}
a & b & a+b+1 \\
b & a+b+1 & a \\
a+b+1 & a & b
\end{array}\right|=3 a b(a+b+c)-a^{3}-b^{3}-(a+b+1)^{3}=0 \\
\Rightarrow 2 a+2 b+1=0 \text { or } a+b=-\frac{1}{2} .
\end{array}
\]