Final answer:
To find the x-values for which the expression (2x + 5) / (x^2 - 2x -1) does not exist, we solve the quadratic equation in the denominator using the quadratic formula to find its roots, which are the values that make the expression undefined.
Step-by-step explanation:
To determine the values of x for which the expression (2x + 5) / (x2 - 2x - 1) does not exist, we must identify the values that make the denominator equal to zero, since division by zero is undefined. A quadratic equation of the form ax2 + bx + c = 0 can be solved using the quadratic formula, which is given by x = (-b ± √(b2 - 4ac))/(2a). In our case, a is 1, b is -2, and c is -1. Using the quadratic formula, we find that the denominator is zero when x equals the roots of the quadratic equation x2 - 2x - 1. Therefore, the expression does not exist for these specific values of x.