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!