To simplify the expression involving a natural logarithm:

\[
\ln\left(\frac{x+1}{x}\right)
\]

we can use logarithmic properties.

### Step-by-Step Solution

1. **Apply the Quotient Rule of Logarithms:**

   The quotient rule for logarithms states that:

   \[
   \ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b)
   \]

   Applying this to the given expression:

   \[
   \ln\left(\frac{x+1}{x}\right) = \ln(x+1) - \ln(x)
   \]

2. **Result:**

   The simplified form of the expression is:

   \[
   \ln(x+1) - \ln(x)
   \]

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

### Related Questions:
1. What are the properties of logarithms, and how are they derived?
2. How can you differentiate the function \(\ln(x+1) - \ln(x)\)?
3. What is the integral of \(\ln(x+1) - \ln(x)\)?
4. How does the change of base formula work for logarithms?
5. Can logarithmic functions be used to model real-world phenomena?

**Tip:** Remember that logarithmic rules, like the quotient rule, are powerful tools for simplifying expressions!

Discover how to simplify the logarithmic expression ln((x+1)/x) using the quotient rule. This problem explores key logarithmic concepts and provides a step-by-step solution. Suitable for high school students in Grades 10-12.

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