which of the following is a rational expression whose domain has a restriction of x ≠ -1?
x+1/x^3
6x^3+60/x
x^2+6x+5/6x+6
The rational expression that has a domain restriction of x ≠ -1 is:
(x^2+6x+5)/(6x+6)
The rational expression whose domain has a restriction of x ≠ -1 is (6x^3+60)/x.
To find the rational expression whose domain has a restriction of x ≠ -1, we need to identify the expression that doesn't allow x to be equal to -1.
Let's analyze the given options one by one:
1. x + 1/x^3
This expression does not have any restriction on the domain. x can take any real value, including x = -1.
2. 6x^3 + 60/x
Similarly, this expression does not have any restriction on the domain. x can take any real value, including x = -1.
3. (x^2 + 6x + 5) / (6x + 6)
Here, the expression involves a fraction with a denominator of 6x + 6. To find the restriction, we need to set the denominator equal to zero and solve for x:
6x + 6 = 0
6x = -6
x = -1
We found that x = -1 satisfies the equation 6x + 6 = 0, which means x = -1 is the restriction for this expression.
Therefore, the rational expression with the domain restriction x ≠ -1 is (x^2 + 6x + 5) / (6x + 6).