To evaluate the expression \(\frac{x+2}{x+1}\) at \(x = -3\), substitute \(-3\) for \(x\) in the equation:

\[
\frac{-3+2}{-3+1}
\]

Now, calculate each part:

1. Calculate the numerator:
   \[
   -3 + 2 = -1
   \]

2. Calculate the denominator:
   \[
   -3 + 1 = -2
   \]

3. Divide the numerator by the denominator:
   \[
   \frac{-1}{-2} = \frac{1}{2}
   \]

So, the value of the expression \(\frac{x+2}{x+1}\) at \(x = -3\) is **\(\frac{1}{2}\)**.

Would you like any further explanation or have any questions?

Here are 5 related questions to explore further:
1. What is the value of \(\frac{x+2}{x+1}\) at \(x = 1\)?
2. How does the expression \(\frac{x+2}{x+1}\) behave as \(x\) approaches \(-1\)?
3. What are the asymptotes of the function \(y = \frac{x+2}{x+1}\)?
4. How would you solve the equation \(\frac{x+2}{x+1} = 2\)?
5. What is the domain of the function \(y = \frac{x+2}{x+1}\)?

**Tip:** When evaluating a rational expression, ensure that the denominator is not zero, as division by zero is undefined.

Learn how to evaluate the rational expression (x+2)/(x+1) at x = -3 with a detailed step-by-step solution. This problem covers rational expressions and substitution methods in algebra. Suitable for high school students.

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