MAT 117 /MAT117 Week 4 Discussion Question
Week 4 DQ 3
What defines a rational expression? How would you explain this concept to someone unfamiliar with it? Do all rational equations have a single solution? Why is that so? Is there such a thing as an irrational exponent? Explain.
The determination of a rational expression is the ratio of one polynomial in relation to another. Rational expressions are just as traditional fractions in that they show portions. In explaining the concept to someone unfamiliar, this is the basis from where AI might start. It is always good to find common ground to explain anything. Common ground here would lie in the comforts held in fraction awareness. I'd use the familiarity in order to build a referendum with rational expressions. The honest answer might be "yes" all rational equations have a single solution. After all a solution is a solution ...right? Wrong! Because rational equations involve variables, multiple solutions are possible. Different values might be plugged into the variables creating sorted outcomes in the solution. There is such a thing as an irrational exponent. I will leave documentary at this time to those better suited to explain this phenom but casual observation leads me to believe that variables play a role inn this happening because there lies no common logic to say...exponents of x and 4. Please feel free, class, to help enlighten your friend on this one.
A rational expression can be summed up quite simply (no pun intended :) It is merely a ratio between two polynomials. If I had to explain the visual basics of a rational expression to someone not in algebra, I would say that it is two separate expressions set up like a fraction (ratio), each generally containing a variable and sometimes an exponent. And as we learned over the last few weeks, a polynomial is an expression containing a variable that is added, subtracted, or multiplied. However, there are some rules for rational expressions, much like many other expressions in algebra.
For example, rational expressions cannot contain a fraction within the ratio, like:
___2___ 3 + 1 x
Additionally, rational expressions cannot contain square roots, like (the red symbol being the square root):
15 + /¯ z z - 5
An irrational exponent, I believe, would be a number or variable with a positive or negative power that is in ratio form (fraction). Please feel free to correct me if I am wrong, but I think it would look something like this:
x^m/n (m/n being the raised exponent). After doing some research on the internet, I really could not find a basic answer to the probability of solving such problems. Some say that it can be done, but others say that it cannot. Kathryn, what are your thoughts?? Could you shed some light on this topic for us? :)
One interesting thing about rational expressions, and Michael said this quite well in his DQ post, is that there are no single solutions for rational expressions. In fact, any expression can have any solution, unless we know exactly what the variable(s) are equivalent to. For example, take the simple algebraic expression x + 1... we have no idea what it equals because we don't know the value of x. The same concept applies to rational expressions.
A rational expression is a set of polynomials that are set up as a ratio (fraction). Rational expressions usually contain variables, real numbers, and sometimes exponents. In explaining the concept of rational expressions to someone that did not know much about algebra I am not sure how I would proceed. I suppose I would say that rational expressions are expressions that are organized and solved like fractions.
Rational expressions can have many solutions. Like the others brought up, whenever you have variables, you open the expression up to numerous possible solutions. I have seen people get