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The given limit problem is:

\[
\lim_{{x \to 2}} \frac{{x^2 + 5x - 14}}{{x^2 + 5x - 14}}
\]

### Solution:
1. First, notice that the numerator and the denominator are exactly the same expression, which simplifies the problem.
2. As long as the denominator is non-zero, the fraction simplifies to:

\[
\frac{{x^2 + 5x - 14}}{{x^2 + 5x - 14}} = 1
\]

3. However, we need to check the value of the denominator at \(x = 2\) to ensure it is not zero:

\[
x^2 + 5x - 14 = (2)^2 + 5(2) - 14 = 4 + 10 - 14 = 0
\]

4. Since the denominator equals zero at \(x = 2\), the expression is undefined at \(x = 2\). Therefore, the limit does not exist in the conventional sense.

Thus, the limit **does not exist** because the expression becomes undefined at \(x = 2\).

Do you have any questions or would you like more details? Here are some related questions for practice:

1. What does it mean for a limit to be undefined?
2. Can limits exist even when the function is undefined at a point?
3. How do you handle limits where both the numerator and denominator approach zero?
4. What are some strategies for solving more complicated limits?
5. How can we use L'Hôpital's Rule to evaluate indeterminate forms?

**Tip:** Always check whether a function is defined at the point you're evaluating the limit!

Find the limit: lim (x→2) (x^2 + 5x - 14) / (x^2 + 5x - 14)

Learn how to solve the limit problem lim (x→2) (x^2 + 5x - 14) / (x^2 + 5x - 14). This step-by-step solution covers important limit concepts and explains why the limit does not exist at x = 2.

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