Problem 70 - College Algebra

Question

What is a rational expression?

Step-by-Step Solution

Answer

A rational expression is a mathematical expression that is the ratio of two polynomials. An example is \(\frac{3x^2 - 2x + 7}{x^3 - 1}\). The polynomial in the denominator should not be zero.

Step 1: Define Polynomial

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer powers of variables. An example of a polynomial is \(3x^2 - 2x + 7\).

Step 2: Define Ratio

A ratio is a relationship between two numbers of the same kind. In mathematics, it is simply a fraction where we divide one quantity by another quantities of the same unit. An example is the ratio between 4 and 7, which can be written as \(\frac{4}{7}\).

Step 3: Define Rational Expression

A rational expression, as per the definitions in Step 1 and 2, is an expression of the ratio of two polynomials, where the polynomial in the denominator is not zero. An example of a rational expression is \(\frac{3x^2 - 2x + 7}{x^3 - 1}\).