Introduction to Algebraic Fractions
Date: 05/29/2008 at 06:45:49 From: Autumn Subject: Algebraic fractions and its problems. What are algebraic fractions? My teacher explained this in school but I still do not understand what algebraic fractions are. Can you help me?
Date: 05/29/2008 at 08:48:35 From: Doctor Ian Subject: Re: Algebraic fractions and its problems. Hi Autumn, A fraction is just a division we haven't done yet. So, for example, 3/4 means "3 divided by 4, whatever that would be". If we have algebraic expressions in place of constants, like x/3 or (x^2 - 4)/(x + 2) then we have an "algebraic fraction". But that's not a big deal. They're just like any other fractions, i.e., they follow the same rules. For example, if we have a fraction like 6/15, we can reduce it by identifying common factors in the numerator and denominator: 6 3 * 2 2 -- = ----- = - because the 3's cancel 15 3 * 5 5 Does that look familiar? We can do the same thing with a fraction like 6x^3 3 * 2 * x * x * x 2x ----- = ----------------- = -- 15x^2 3 * 5 * x * x 5 There's only one important difference here. Recall that we can't divide by zero. That's not a problem with a fraction like 6/15, where we know all the values... but with a fraction like (6x^3)/(15x^2), we have to keep track of the fact that x can't ever be equal to zero. Even if the simplified form (2x)/5 would allow that, the original form wouldn't. With quadratic and higher polynomials, we can get these kinds of cancellations by factoring them into products of binomials, e.g., x^2 - 4 (x + 2)(x - 2) x - 2 ------------ = -------------- = ----- x^2 + 5x + 6 (x + 2)(x + 3) x + 3 Again, we need to keep in mind that BOTH -2 and -3 are prohibited values for x in the original expression. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 05/29/2008 at 09:48:11 From: Autumn Subject: Thank you (Algebraic fractions and its problems.) Thank you for that. It really did help and i can manage my homework better! Thanks again.
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