Problema Solution
What are rational expressions? Why must we always be mindful of the final value of the denominator in a rational expression? Post AND SOLVE an example of a rational expression that yields zero in the denominator. Please note: for this discussion question, please solve your rational expression example to demonstrate how it yields zero in the denominator.
Answer provided by our tutors
(a) A polynomial expression is an expression having one or more terms in which the
variable has non-negative integer powers. For example P(x) = x^3 + 6x^2 - 8x + 3
A rational expression is a ratio of two polynomial expressions. This is the
uniqueness of a rational expression.
For example R(x) = P(x)/Q(x) = (x + 7)/(x^3 - 9)
(b) We know that a rational expression has a polynomial numerator and a polynomial
denominator. In many cases, these polynomials can be factored. Therefore, to
reduce a rational expression to its simplest form, we need to factor the numerator
and denominator, and cancel out any common factors between them. That's why
factoring is an important part of simplifying a rational expression
(c) We must be mindful about the values the final denominator of a rational
expression can take, because such values must not be 0.
3x/(x^2 - 16) = 3x/{(x + 4)(x - 4)}
Here, x can't take the values -4, 4 because if it does, then the denominator becomes
0 and the retaional expression becomes undefined.