Unit 7
–
Rational Expressions
and Equations
Module 7A
Sections 20.1
–
20.3

7A
Multiplying and Simplifying Rational
Expressions
Find all numbers for which a rational expression is not defined.
2
Rational numbers are quotients of integers.
The following are called
rational
expressions or
fraction
expressions.
They are quotients, or ratios, of
polynomials:

7A
Multiplying and Simplifying Rational
Expressions
Find all numbers for which a rational expression is not defined.
3
A rational expression is also a division. For example,

7A
Multiplying and Simplifying Rational
Expressions
Find all numbers for which a rational expression is not defined.
4
When a variable is replaced with a number that
produces a denominator equal to zero, the rational
expression is not defined.
For example, in the expression
when
x
is replaced with 2 the denominator is 0, and the
expression is not defined:

7A
Multiplying and Simplifying Rational
Expressions
Find all numbers for which a rational expression is not defined.
Example 1
Find all numbers for which the rational expression
is not defined.
5

7A
Multiplying and Simplifying Rational
Expressions
Find all numbers for which a rational expression is not defined.
Example 1
6
The rational expression is not defined for the
replacement numbers 5 and
–
2.
Solution

7A
Multiplying and Simplifying Rational
Expressions
Simplify rational expressions by factoring the
numerator and the
denominator and removing factors of 1.
7
In algebra, instead of simplifying a fraction like
we may need to simplify an expression like
To simplify, we can do the reverse of multiplying. We
factor the numerator and the denominator and “remove”
a factor of 1.

7A
Multiplying and Simplifying Rational
Expressions
Simplify rational expressions by factoring the
numerator and the
denominator and removing factors of 1.

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- Winter '15
- Kitnip
- Rational Expressions, Equations, Fractions, Integers, Fraction, Elementary arithmetic, Greatest common divisor, Least common multiple, Multiplicative inverse