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### Algebra: Factoring Fractions

```
Date: 07/30/97 at 02:13:05
From: Wendy Herndon
Subject: Algebra 2

8ab                16b2
------  divided by  ---------
4a2-b2             8a2 - 4ab

My sister showed me how to do this but I couldn't understand. I think
where I'm stuck is where it came to factoring.

If you could help me I'd be so happy.

Thanks, Wendy
```

```
Date: 07/30/97 at 07:43:38
From: Doctor Anthony
Subject: Re: Algebra 2

When dividing by a fraction, you can write it more clearly by
MULTIPLYING by that fraction turned upside down. So the whole
expression is:

8ab           8a^2 - 4ab
-----------  x  ------------
4a^2 - b^2          16b^2

The term  (4a^2-b^2)  is a difference of squares and factorizes to
(2a-b)(2a+b).  You can prove this to your own satisfaction by
multiplying out the two brackets:

(2a-b)(2a+b) =  4a^2 + 2ab - 2ab - b^2  =  4a^2-b^2

8ab x 4a(2a - b)            32a^2.b(2a-b)
------------------    =    ------------------
(2a-b)(2a+b) x 16b^2        16b^2(2a-b)(2a+b)

Now you can cancel any terms that are common to the top and bottom
lines. The bracket (2a-b) occurs on both lines and can be cancelled.
The number 32 on the top line is reduced to 2 by the 16 on the bottom
line. Also there is a factor b on both lines, and this can be
cancelled. After these cancellations we get:

2a^2
---------
b(2a+b)

This is as far as the simplification can be taken.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Factoring Expressions

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