Sure! To understand the expression [tex]\(\frac{x+5}{x^2-2}\)[/tex] more clearly, let's break it down step-by-step.
1. Identify the Numerator and Denominator:
- The numerator is the term on the top of the fraction, which is [tex]\(x + 5\)[/tex].
- The denominator is the term on the bottom of the fraction, which is [tex]\(x^2 - 2\)[/tex].
2. Definition of a Rational Function:
- A rational function is a function that can be expressed as the quotient (or division) of two polynomials. In this expression, both [tex]\(x+5\)[/tex] and [tex]\(x^2 - 2\)[/tex] are polynomials.
3. Quotient of Two Polynomials:
- The expression [tex]\(\frac{x+5}{x^2-2}\)[/tex] indicates that [tex]\(x+5\)[/tex] is being divided by [tex]\(x^2-2\)[/tex].
Therefore, the expression [tex]\(\frac{x+5}{x^2-2}\)[/tex] is accurately described as "the quotient of [tex]\(x+5\)[/tex] and [tex]\(x^2-2\)[/tex]."
So, the correct statement is:
C. The quotient of [tex]\(x + 5\)[/tex] and [tex]\(x^2 - 2\)[/tex].
This means that the fraction [tex]\(\frac{x+5}{x^2-2}\)[/tex] represents dividing the polynomial [tex]\(x+5\)[/tex] by the polynomial [tex]\(x^2-2\)[/tex].
