a. \( \quad x^{2}-3 x+4 \pm 10 /(x+1) \)

Let's break down the expression! The term \( \pm 10/(x+1) \) adds a twist to things since it introduces a variable component that can create different scenarios depending on whether you take the positive or negative value. This means that instead of just solving a straightforward quadratic, you're actually looking at two different functions: one where you’re adding the fraction and one where you’re subtracting it. It's like splitting your personality into two distinct characters—cool, right? Now, a common mistake here is forgetting to consider the domain of the function due to the denominator \( (x + 1) \). If you set \( x = -1 \), the expression becomes undefined, so always check for restrictions before diving into solving or graphing this function. Happy calculating, but keep an eye out for those pesky undefined points!