The image shows the following limit problem:

$\text{a. } \lim_{x \to 1} \frac{x^2 + 2x - 3}{2x - 3}$

Let's solve this limit step by step.

Step 1: Direct Substitution

First, we try to directly substitute $x = 1$ into the expression.

$\frac{(1)^2 + 2(1) - 3}{2(1) - 3} = \frac{1 + 2 - 3}{2 - 3} = \frac{0}{-1} = 0$

Step 2: Analyze the Result

Since direct substitution gives us a defined value (0), the limit exists and is equal to 0.

Thus, the solution is:

$\lim_{x \to 1} \frac{x^2 + 2x - 3}{2x - 3} = 0$

Would you like more details, or do you have any questions?

Here are five related questions:

1. How do you solve limits that involve indeterminate forms like $\frac{0}{0}$?
2. What are some techniques for simplifying complex limit expressions?
3. Can L'Hôpital's Rule be applied to this problem?
4. How do you determine if a limit does not exist?
5. What is the significance of limits in calculus?

Tip: When you substitute a value into a limit and get $\frac{0}{0}$, you often need to factor and simplify the expression before taking the limit again.