Questions: 1. a. What does the term rational mean in "rational number" and "rational expression"? (Value: 1 mark) b. Will a rational expression always have at least one non-permissible value? Give an example to support your answer. (Value: 1 mark)

Solution Steps

The term "rational" in "rational number" refers to a number that can be expressed as the quotient or fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\). Similarly, a "rational expression" is an expression that can be written as the quotient of two polynomials, where the denominator is not zero.

A rational expression will not always have non-permissible values, but it often does. Non-permissible values occur when the denominator of the rational expression is equal to zero, as division by zero is undefined. For example, consider the rational expression \(\frac{x+1}{x-2}\). The non-permissible value is \(x = 2\) because it makes the denominator zero.

Final Answer