This document discusses rational expressions and equations. It defines a rational expression as an algebraic expression that can be written as the quotient of two polynomials. An expression is undefined when its denominator is equal to zero, which are called the non-permissible values. The document provides examples of finding non-permissible values and simplifying rational expressions by factoring and cancelling common factors in the numerator and denominator. It concludes with an assignment to complete practice problems related to rational expressions and equations.

1. Rational Expressions and Equations
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2. Rational Expression ­ an algebraic expression that can be written as
the quotient of two polynomials.
Numerator
A
B
Denominator
Where B≠0
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3. Undefined ­ An expression is undefined when its denominator is
equal to zero.
Numerator
A
B
Denominator
Where B≠0
Non­permissible values ­ values of the variable that give a zero
(undefined) value for the denominator.
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4. Example : Find the non­permissible values
a) 3 b) ­ 2
6 x ­ 1
c) 1 d) x
( x2 ­ 4 ) x ­ 5
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5. More Examples:
e) 2 x + 1
x2 ­ 4
f) 2
x3
g) 5
(x ­ 1)3
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6. Simplifying Rational Expressions (Lowest Terms)
We can simplify rational expressions by:
1) Factoring the numerator and the denominator.
2) Divide out any factors that are common to both the numerator and the
denominator.
ie. a) 6 ( 12 )
24
2
b) x_ ( x + 1 )
x ( x + 1 )3
3) The Expression is simplified or reduced if the numerator and the
demoninator have no factors in common except for 1
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7. Example 2 Simplify and state the non­permissible values:
a) 2x c) x2 ­ x
_______
4x
x2 + x ­ 2
b) 3xa2b3
______ d) a ­ b
_______
6ab b2 ­ a2
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8. Assignment
p 158 questions 1­18
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