2. If the function
$$
y=\frac{x+k}{(k+1) x^{2}+(2 k+2) x+2 k-3}
$$

has the domain of the independent variable $x$ as all real numbers, then the range of values for $k$ is $\qquad$
2. $k \leqslant-1$ or $k>4$.

Notice that
$$
\begin{array}{l}
f(x)=(k+1) x^{2}+(2 k+2) x+2 k-3 \\
=(k+1)(x+1)^{2}+k-4 .
\end{array}
$$

When $k=-1$, $f(x)=-5 \neq 0$, which satisfies the condition.
When $k \neq-1$,
$$
f(x) \neq 0 \Rightarrow k+1 \text{ and } k-4 \text{ have the same sign. }
$$

Thus, $k4$.
Therefore, the range of $k$ is $k \leqslant-1$ or $k>4$.