Final answer:
To find the range of the expression x² - x+ 1 / x²+ x + 1, we can take the derivative, find the critical points, and evaluate the expression at these points.
Step-by-step explanation:
The range of the expression x² - x+ 1 / x²+ x + 1 can be determined by finding the minimum and maximum values it can take. To find the minimum and maximum values, we can take the derivative of the expression with respect to x and set it equal to zero. Solving this equation will give us the critical points. Evaluating the expression at these critical points and at the endpoints of the given domain will give us the range of the expression.