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Cancelling Algebraic Fractions

```Date: 11/11/2002 at 07:17:15
From: Dean James
Subject: Algebraic fractions

I am currently doing some last day revision for my maths GCSE (Higher
Tier), which I will be taking over this week.

I have looked through all of my study materials, but I still don't
understand how to cancel down algebraic fractions, as they don't
explain it very thoroughly.

Thanking you in anticipation,
Dean James
```

```
Date: 11/11/2002 at 10:19:39
From: Doctor Ian
Subject: Re: Algebraic fractions

Hi Dean,

It's basically the same idea as reducing other kinds of fractions
using prime factors. For example, here's how to do it using only
numbers:

72   2 * 2 * 2 * 3 * 3        2   2   3   2 * 3
-- = ---------------------- = - * - * - * ----- = 6/5
60       2 * 2 * 3     * 5    2   2   3     5

You can do exactly the same thing using variables as your 'prime
factors':

x^3 y^4 z     x * x * x * y * y * y * y * z
----------- = -----------------------------------------
x   y^2 z^4           x * y * y         * z * z * z * z

x * x * y * y
= -------------
z * z * z

x^2 y^2
= -------
z^3

Eventually, as you get more practice with this, you'll notice that you
can accomplish the same thing just by subtracting exponents:

x^3 y^4 z
----------- = x^(3-1) y^(4-2) z^(1-4) = x^2 y^2 z^-3
x   y^2 z^4

The other kind of cancellation that often occurs requires you to
factor polynomials, e.g.,

x^2 + 3x + 2   (x+1)(x+2)   (x+1)   (x+2)
------------ = ---------- = ----- * ----- = (x+2)/(x-1)
x^2 - 1     (x+1)(x-1)   (x+1)   (x-1)

But it's all really the same thing: Break the numerator and
denominator into the most basic possible factors; and eliminate any
factor that appears in both the numerator and the denominator.

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Factoring Expressions

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