1. We are asked to simplify the expression $$\frac{x^2 + x + 2}{x - 1}$$. 2. The expression is a rational function where the numerator is a quadratic polynomial and the denominator is a linear polynomial. 3. To simplify, we check if the numerator can be factored and if any factors cancel with the denominator. 4. The numerator is $$x^2 + x + 2$$. We look for factors of 2 that add up to 1 (the coefficient of $x$), but since 2 and 1 do not satisfy this, the quadratic does not factor nicely over the integers. 5. Since the numerator does not factor to include $(x-1)$, the expression cannot be simplified by canceling. 6. Therefore, the simplified form remains $$\frac{x^2 + x + 2}{x - 1}$$. 7. Note: The expression is undefined at $x=1$ because the denominator becomes zero. Final answer: $$\frac{x^2 + x + 2}{x - 1}$$