27. $y=\frac{x^{2}-5 x+4}{x^{2}+x+1}$.

27. $y=\frac{x^{2}-5 x+4}{x^{2}+x+1}$.
Solution. By setting the denominator of the fraction to zero and solving the resulting quadratic equation $x^{2}+x+1=0$, we can verify that its roots are complex numbers: $x=-\frac{1}{2} \pm i \frac{\sqrt{3}}{2}$. The denominator does not become zero for any real value of $x$. Therefore, the function is defined for all real values of $x$. Its domain is the infinite interval $(-\infty, \infty)$.