Rational ExpressionsDate: 01/06/2002 at 20:33:56 From: Ashley Subject: Rational Expressions Hello, Basically I just need some help on rational expressions in general. My main problems are: 1) How do I know when I need to factor and when I don't, and if there are the same polynomials, trinomials, etc., can I cancel them out at all times? 2) What are the restrictions on simplified expressions? I always seem to do something wrong. Thanks for your help. Ashley Townsend Date: 01/07/2002 at 09:24:35 From: Doctor Ian Subject: Re: Rational Expressions Hi Ashley, The answer to your first question is: You want to factor whenever you can. In the best case, it helps you identify terms that cancel each other out; in the worst case, you end up with an expression whose meaning is more plainly visible. The answer to your second question is: You can never, ever, under any circumstances, divide by zero. What makes this tricky is that you might start with an expression like: x^2 - 7x + 12 ------------- x - 3 and simplify it like this: x^2 - 7x + 12 (x - 3)(x - 4) ------------- = -------------- = x - 4 x - 3 (x - 3) Now, what does this _mean_? It means that at any value of x EXCEPT 3, you can use the simple expression (x - 4) in place of the more complicated expression (x^2 - 7x + 12)/(x - 3). But the original expression is undefined at x = 3, so the simpler expression - when used in place of the complicated expression - is also undefined there. (Think of it this way. Suppose I lend you my car, and I say: You can do whatever you want, as long as you don't drive the car in New Jersey. Now, suppose you lend the car to a friend. You have to tell him that HE can't drive it in New Jersey, either! And if he lends the car to another friend, he has to pass the warning along.) To keep track of this kind of thing, whenever you cancel out something like (x - 3) from a denominator, you can make a note off to the side, to help you remember the exceptions later on: x^2 - 7x + 12 (x - 3)(x - 4) ------------- = -------------- x - 3 (x - 3) = (x - 4) [undefined at x = 3] If I haven't addressed your question completely, please write back with some specific examples that are giving you trouble. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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