Rational Functions, algebra homework help

1. OPEN ENDED Write two rational expressions that are equivalent.
2. OPEN ENDED Write two polynomials that have a LCM of d3 – d.

Writing in Math 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

462
GET READY for the Lesson
Peanuts
Add
x lb of
peanuts.
cu
50
85 or of the
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.
8.
Therefore,
of the
mixture is peanuts. If the store
manager adds an additional
x pounds of peanuts to the
8 + x
mixture, then of the
13 + x
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 it 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.
EXAMPLE
Simplify a Rational Expression
1
2x(x – 5)
a. Simplify
(x – 5)(2-1)
Look for common factors.
2x(x – 5)
2x_..*-5
(x – 5)(x2 – 1) 2 – 1
How is this similar to simplifying 15
2x
Simplify
12 – 1
b. Under what conditions is this expression undefined?
Just as with a fraction, a rational expression is undefined if
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