https://file.aiquickdraw.com/mathbot/file/1724077914279xc5shx8g.jpg

Solve this math, please double-check it. And take step by step to understand 

The expression in the image is:

\[
\lim_{{x \to 3}} \left(\frac{1}{x+1} - \frac{1}{4}\right)
\]

Let's solve this step by step.

### Step 1: Evaluate the limit by substituting \(x = 3\)

Substitute \(x = 3\) into the expression:

\[
\lim_{{x \to 3}} \left(\frac{1}{x+1} - \frac{1}{4}\right) = \frac{1}{3+1} - \frac{1}{4}
\]

### Step 2: Simplify the expression

First, simplify the terms inside the limit:

\[
\frac{1}{3+1} = \frac{1}{4}
\]

So, the expression becomes:

\[
\frac{1}{4} - \frac{1}{4}
\]

### Step 3: Subtract the fractions

Since the fractions have the same denominator, subtract the numerators:

\[
\frac{1-1}{4} = \frac{0}{4} = 0
\]

### Final Answer

The limit is:

\[
\lim_{{x \to 3}} \left(\frac{1}{x+1} - \frac{1}{4}\right) = 0
\]

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

### Relative Questions:
1. What is the importance of evaluating limits in calculus?
2. How does the concept of continuity relate to limits?
3. Can limits be used to find the derivative of a function?
4. What happens if the limit involves an indeterminate form like \( \frac{0}{0} \)?
5. How do you apply L'Hôpital's rule to solve complex limits?

### Tip:
When dealing with limits, always check if direct substitution is possible before considering more advanced techniques like factoring or L'Hôpital's rule.

Learn how to solve the limit problem: limit as x approaches 3 of (1/(x+1) - 1/4) with a step-by-step solution. This problem covers key calculus concepts, including limits and their properties. Suitable for college-level students.

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