Which of the following is a rational expression whose domain has a restriction of x≠−1?

1 answer

To create a rational expression with a domain restriction of \( x \neq -1 \), we need to include a factor in the denominator that will equal zero when \( x = -1 \). This can be achieved by using \( x + 1 \) in the denominator.

An example of a rational expression with this restriction is:

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

In this case, the denominator \( x + 1 \) equals zero when \( x = -1 \), which means the expression is undefined at that value. Therefore, the domain of this expression is all real numbers except \( -1 \).

You can also create variations, such as:

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

or

\[ \frac{3x}{x + 1} \]

In each case, the domain restriction remains \( x \neq -1 \).