Question

Which of the following is true about rational expressions?

a) x^2 - x + 1 is not a rational expression.
b) The degree of the numerator is less than the degree of the denominator in a proper rational expression.
c) Rational expressions can be defined when the denominator is zero, as long it has at least one real solution.
d) x/(x+3) is a proper rational expression.

Answer 1

Option (b) is true, stating that in a proper rational expression, the degree of the numerator is less than the degree of the denominator. Options (a), (c), and (d) are incorrect regarding the nature of rational expressions and when they can be defined.

Step-by-step explanation:

The correct answer to the question about rational expressions is that (b) The degree of the numerator is less than the degree of the denominator in a proper rational expression is true. A rational expression is a ratio of two polynomials and can be categorized as proper if the degree of the numerator is less than the degree of the denominator. Choice (a) is incorrect because x^2 - x + 1 is a polynomial, not expressed as a ratio of polynomials. Choice (c) is wrong since rational expressions cannot be defined for values that make the denominator zero; these points are known as discontinuities or undefined points. For choice (d), x/(x+3) indeed represents a proper rational expression.