Question

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

x2+6x+56x+6
Start Fraction x squared plus 6 x plus 5 over 6 x plus 6 End Fraction

x+1x3
Start Fraction x plus 1 over x cubed End Fraction

6x3+60x
Start Fraction 6 x cubed plus 60 over x End Fraction

x√2x+2
Start Fraction Start Root x End Root over 2 x plus 2 End Fraction

Answer 1

To identify which rational expression has a domain restriction of \( x \neq -1 \), we need to find which one has a factor in the denominator that equals zero when \( x = -1 \).

Let's analyze each option:

1. **\( \frac{x^2 + 6x + 5}{6x + 6} \)**:
- The denominator \( 6x + 6 = 6(x + 1) \) equals zero when \( x = -1 \). This expression has a restriction of \( x \neq -1 \).

2. **\( \frac{x + 1}{x^3} \)**:
- The denominator \( x^3 \) equals zero at \( x = 0 \). There is no restriction from \( x = -1 \).

3. **\( \frac{6x^3 + 60}{x} \)**:
- The denominator \( x \) equals zero at \( x = 0 \). There is no restriction from \( x = -1 \).

4. **\( \frac{\sqrt{x}}{2x + 2} \)**:
- The denominator \( 2x + 2 = 2(x + 1) \) also equals zero when \( x = -1 \), but the square root in the numerator imposes a restriction of \( x \geq 0 \) for real values to be defined.

Only the first option, **\( \frac{x^2 + 6x + 5}{6x + 6} \)** contains a restriction of \( x \neq -1 \) based on the denominator. Thus, the answer is:

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