3. If the function $y=\frac{k x+5}{k x^{2}+4 k x+3}$ has the domain of all real numbers, then the range of real number $k$ is $\qquad$
$3.0 \leqslant k0$  when, from $k x^{2}+4 k x+3=k(x+2)^{2}+3-$ $4 k$, we know that to make it never zero, then $x$ can take any real number.
$\because k(x+2)^{2} \geqslant 0, \therefore$ it is only necessary that $3-4 k>0$, i.e., $k<\frac{3}{4}$, which contradicts $k<0$, indicating that this situation cannot hold. Therefore, the range of real number $k$ is $0 \leqslant k<\frac{3}{4}$.