rational expressions, algebra homework help

Use the information about rational expressions on

page 462

to explain how rational expressions are used in mixtures. Include an example of a mixture problem that could be represented by .

8-1
Multiplying and Dividing
Rational Expressions
Main Ideas
• Simplily rational
expressions
• Simplify complex
fractions
Peanuts
Add
x lb of
peanuts
New Vocabulary
rational expression
complex traction
GET READY for the Lesson
The Goodie Shoppe sells
candy
and nuts by the pound. One
item is a mixture made with
8 pounds of peanuts and
5 pounds of cashews.
Therefore, 545 or of the
mixture is peanuts. If the store
manager adds an additional
x pounds of peanuts to the
mixture, then
8+
13+*
of the
mixture will be peanuts.
8 lb of peanuts
5 lb of cashews
– 13 lb of nuts
NUTS
Simplify Rational Expressions A ratio of two polynomial expressions
such as 1+ is called a rational expression. Because variables in
algebra often represent real numbers, operations with rational numbers
and rational expressions are similar.
To write a fraction in simplest form, you divide both the numerator and
denominator by their greatest common factor (GCF). To simplify a
rational expression, you use similar techniques.
EXAMPLESimplify a Rational Expression
a Simplify – 21x – 5)
(x – 5)(2-1)
Look for common factors.
2x(x – 5) 2x
How is this similar to simplifying 1
6 – 5)(2-1)
Simplity
b. Under what conditions is this expression undefined?
Study Tip Just as with a fraction, a rational expression is undefined if
the denominator is equal to 0. To find when this expression
Excluded Values
is undefined, completely factor the original denominator.
Numbers that would
2x(x – 5) 2x(x – 5)
cause the expression
? – 1 (x – 1)(+1)
to be undefined are
(x – 5)(2-1)(-5)(x – 1)6+1)
called excluded
values.
The values that would make the denominator equal to 0 are 5, 1, or
-1. So the expression is undefined when x = 5, x = 1, or x = -1.
442 Chapter 8 Rational Expressions and Equations