Final answer:
The student's equation is a rational expression because it consists of ratios of polynomials.
Step-by-step explanation:
The question 'How do you know if it's a rational expression?' falls under the subject of mathematics, specifically rational expressions and equations. A rational expression is one that can be expressed as a ratio of two polynomials, where the denominator is not equal to zero. The given equation -8/x + 2x+1/2x = 1/2 includes terms that are ratios of polynomials, thus classifying it as a rational expression.
To verify if an expression is equal to some value, we need to maintain equality by performing the same operations on both sides of the equation. As mentioned, when the numerator and the denominator are the same, the fraction equals 1. This principle is used to simplify fractions or to solve equations involving fractions. Moreover, understanding the relationship between multiplication and division, such as dividing by a number being equivalent to multiplying by its reciprocal, plays a crucial role in solving these equations.
Another aspect of working with rational expressions is finding a common denominator when adding or subtracting fractions. This involves understanding how to manipulate fractions to have the same denominator, often by multiplying the denominators. Once a common denominator is established, the numerators can be directly combined.