27. For what values of $\boldsymbol{a}$ is the inequality $-3<\frac{x^{2}+a x-2}{x^{2}-x+1}<2$ true for all values of $x$?

In № $28-32$ solve the inequalities.
27. $x^{2}-x+1>0$ for any $x$.

Then $\left\{\begin{array}{l}-3\left(x^{2}-x+1\right)<0 \\ x^{2}+a x-2<0 .\end{array}\right.$

Both inequalities are valid for any $x$ if the discriminants of the quadratic polynomials are negative, i.e.

$$
\begin{aligned}
& (a-3)^{2}-16<0, \quad|a-3|<4,-1<a<7 \\
& (a+2)^{2}-16<0, \quad|a+2|<4,-6<a<2
\end{aligned}
$$

Conclusion: $-1<a<2$.