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In response to yequalsx: I see 2 applications of rational expressions off the top of my head: 1) From an abstract viewpoint, the message is "We can do the same
by yaks_hairbrush 17y ago
In response to yequalsx:
I see 2 applications of rational expressions off the top of my head:
1) From an abstract viewpoint, the message is "We can do the same stuff with polynomials that we do with integers. The only issue is that factoring is harder." This message gets very garbled
2) Solving ratio problems A/B = C/D come up very often. For example: I've won 43/87 freecell games. How many in a row do I have to win to get to 70%?
- yequalsx 17y agoI agree with both of these examples. And here is my point. The sort of practical applications of rational functions involve very simple rational functions. So if our motivation comes solely from word problems then the natural question is why are we learning to manipulate ( x^2 + 2xy + y^2)/(x - y) + 1/(x^2 - y^2) Has there ever occurred a practical application in which this expression has come up? If our motivation is expanding our understanding of manipulating algebraic objects then this expression is very much a practical application. It's an extension of an existing idea - rational numbers - to a new class of objects. Be able to do this sort of abstraction is useful in mathematics, and in fact is the essence of mathematical thought. It's also useful in things like programming.
- dhimes 17y agoThe motivation for learning to manipulate rational expressions has to come well before you get to this.