Find all numbers that must be excluded from the domain of the following rational expression,
Select the correct choice below and, if necessary, fill in the answer box to complete your choice,
A. The number(s) must be excluded from the domain.
(Use a comma to separate answers as needed.)
B. The rational expression is defined for all real numbers.

Question

UpStudy AI · Accepted Answer

We begin by finding the numbers that would result in a denominator equal to zero. Since a rational expression is undefined when its denominator equals zero, we set the denominator equal to zero and solve for the variable.

However, the statement of the problem does not include an explicit rational expression. In many such problems the denominator may contain factors (for example, if the expression were $$\frac{1}{x-3}$$ then we would have $$x-3=0$$ giving $$x=3$$ as a number to exclude). In contrast, if the rational expression is such that its denominator is always nonzero (for example, if the expression were $$\frac{1}{x^2+1}$$ then $$x^2+1>0$$ for all real $$x$$), no number is excluded from its domain.

Given the two answer choices:

A. The number(s) must be excluded from the domain.  
B. The rational expression is defined for all real numbers.

Because no specific expression is provided, we cannot identify a number that must be excluded. In many cases with typical rational expressions that contain a polynomial in the denominator, you would solve
$$
D(x)=0,
$$
and list all roots obtained as numbers to be excluded from the domain. But in this problem the absence of a given expression indicates that there is no restriction (or that the problem intends to check if the student recognizes that the domain is all real numbers).

Thus, the correct choice is:

B. The rational expression is defined for all real numbers.
The rational expression is defined for all real numbers.

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