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### Simplifying Rational Expressions

```Date: 06/13/2002 at 13:01:38
From: Jason
Subject: what does this mean

I was wondering, in this question

Find (-6x^2 - 4xy + 8x)/(2x)

do they want me to find out what the variables are, or do they want me
to do something else with it?  That is the exact way they have the
question written down.
```

```
Date: 06/13/2002 at 13:29:20
From: Doctor Mike
Subject: Re: what does this mean

Jason,

They want you to simplify the expression.  You can factor 2x out of
the numerator, so that the numerator is

2x(-3x - 2y + 4)

Then, for any non-zero x, the original expression is
equal to (-3x - 2y + 4).

Maybe I should add just a little to this.  When you factor
the numerator, then the expression becomes

(2x)*(-3x-2y+4)/(2x)

At this point you might want to say "Sure, just cancel the
2x terms".  That is correct, but the reason you can cancel
is that (2x)*(-3x-2y+4)/(2x) equals the product of fractions

2x     -3x-2y+4
---- * ----------
2x         1

To see why this is, just think of the rule about how to
multiply fractions together; namely, multiply numerators
together to get the new numerator and multiply denominators
together to get the new denominator.  The step I did above
is sort of like UN-multiplying.  Anyway, once you do that,
it is easy to see that (2x)/(2x) equals one whenever it makes
sense at all, which is when x is not zero.  See?  I hope
this helps.

- Doctor Mike, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 06/13/2002 at 13:34:34
From: Jason
Subject: Thank you (what does this mean)

Thank you for replying so quickly and for explaining the answer really
well.  I understood your response completely.

Thank you again.
```
Associated Topics:
High School Polynomials

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