The domain of the expression x²+2x+1/x+1 is all real number except what numbers?

The domain of a function is determined by identifying any values of the variable \(x\) that would make the function undefined. In the given expression:

\[
\frac{x^2 + 2x + 1}{x + 1}
\]

The denominator cannot be zero, since division by zero is undefined. So, we need to find when the denominator is zero:

\[
x + 1 = 0 \implies x = -1
\]

Thus, the function is undefined when \(x = -1\).

Therefore, the domain of the expression is all real numbers except \(x = -1\).

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Would you like more details or have any other questions?

Here are 5 questions related to this concept:

1. How do you determine the domain of a rational function?
2. What happens when a denominator is zero in a function?
3. Can this function be simplified further by factoring?
4. How do you find the domain of a polynomial function?
5. What is the range of a rational function like this one?

**Tip**: Always check for values that make the denominator zero when finding the domain of rational expressions.

The domain of the expression x²+2x+1/x+1 is all real numbers except what numbers?

Understand how to find the domain of the rational expression x²+2x+1/x+1, focusing on identifying values that make the denominator zero. This step-by-step explanation covers core algebraic concepts such as rational functions and undefined values. Suitable for students in Grades 9-10.

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