WTAMU > Virtual Math Lab > College Algebra > Tutorial 8: Simplifying Rational Expressions
 Answer/Discussion
to 1a
|
| Our restriction is that the denominator of a fraction can never be
equal to 0.
So to find what values we need to exclude, think of what value(s) of
x,
if any, would cause the denominator to be 0. |
 |
*Factor the den. |
| This give us a better look at it.
Since 0 would make the first factor in the denominator 0, then 0
would have to be excluded.
Since 4 would make the second factor in the denominator 0, then 4
would also have to be excluded. |
| Answer/Discussion
to 2a
|
| Step 1: Factor the numerator
and the denominator
AND |
| Step 2: Divide out all
common factors that the numerator and the denominator have. |
| To find the value(s) needed to be excluded from the domain, we need
to ask ourselves, what value(s) of a would
cause our denominator to be 0?
Looking at the denominator a - 4, I would
say it would have to be a = 4. Don't
you agree?
4 would be our excluded value. |
| Answer/Discussion
to 2b
|
| Step 1: Factor the numerator
and the denominator
AND |
| Step 2: Divide out all
common factors that the numerator and the denominator have. |
 |
*Factor
the trinomial in the den.
*Factor out a -1 from (8 - x)
*Divide out the common factor of (x
- 8)
*Rational expression simplified |
Note that 8 - x
and x - 8 only differ by signs, in other words
they are opposites of each other. In that case, you can factor a
-1 out of one of those factors and rewrite it with opposite signs, as shown
in line 3 above.
To find the value(s) needed to be excluded from the domain, we need
to ask ourselves, what value(s) of x would
cause our denominator to be 0?
Looking at the denominator x + 1, I would
say it would have to be x = -1. Don't
you agree?
-1 would be our excluded value. |
WTAMU > Virtual Math Lab > College Algebra > Tutorial 8: Simplifying Rational Expressions
All contents copyright (C) 2002 - 2008, WTAMU and Kim Seward. All rights reserved.
Last revised on Feb. 29, 2008 by Kim Seward.
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