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

To identify a rational expression with a domain restriction of \( x \neq -1 \), we need to determine which expression has the potential for division by zero at \( x = -1 \).

Let's analyze each option:

A. \(\frac{x^2 + 6x + 5}{6x + 6}\)

The denominator \( 6x + 6 = 6(x + 1) \). This expression is undefined when \( x + 1 = 0 \), which occurs at \( x = -1 \). Therefore, this expression has a restriction of \( x \neq -1 \).

B. \(\frac{\sqrt{x}}{2x + 2}\)

The denominator \( 2x + 2 = 2(x + 1) \) also becomes zero when \( x + 1 = 0 \) or \( x = -1 \). Thus, this expression also has a restriction of \( x \neq -1 \).

C. \(\frac{x + 1}{x^3}\)

The expression \( x^3 = 0 \) is only problematic when \( x = 0 \), not at \( x = -1 \). Thus, this expression does not have a restriction of \( x \neq -1 \).

D. \(\frac{6x^3 + 60}{x}\)

The denominator is \( x \), which is undefined at \( x = 0 \) but not at \( x = -1 \). Therefore, this expression does not have a restriction of \( x \neq -1 \).

Both options A and B have the restriction \( x \neq -1 \). However, since all we need is one valid option, we can select option A, as it's the first one found.

**Therefore, the answer is A. \(\frac{x^2 + 6x + 5}{6x + 6}\)**.