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### 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.
```
Associated Topics:
High School Polynomials

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