Name: ______________________________________ Date:________________
Unit 3 Algebra: Cubic, Square Root, and Rational Functions (Red)
Section 3.8 Simplify Rational Expressions Page 161- 164
Essential Question: How do you simplify rational expressions?
Vocabulary:

A _____________ _______________ is an expression that can be written as a ratio of 2 polynomials.

A rational expression is undefined when the denominator is 0. A number that makes a rational expression undefined is called an ___________________ ________________.

A rational expression is in its ____________ ____________ if the numerator and denominator have no factors in common except for 1.
EXAMPLE 1: Find the excluded values, if any, of the expression. 𝑥 a)
3𝑥−9 𝑥
The expression
3𝑥−9 is undefined when
____________ = 0, or x = _________. The excluded value is
________________.
The expression is undefined when b) ___(x+2)__ x 2 + 2x – 15
____________ = 0, or when ( ) (________)= 0. The solutions of the equations are _____ and ______. The excluded values are ______ and ________.
YOU TRY:
1.
__ _7 __
2x 2 - 5x + 6
2.
___(x – 1)__ x 2 - 16

Name: ______________________________________ Date:________________
EXAMPLE 2: Simplify expressions by dividing out monomials.
Simplify the rational expressions, if possible. State the excluded values.
___2m __
8m (m – 1) =
Divide out common factors.
=
Simplify
The excluded values are ______ & _____ .
EXAMPLE 3: Simplify expressions by dividing out binomials.
Simplify the rational expressions, if possible. State the excluded values. x 2 + 4x - 21__
x 2 – 5x + 6
=
Factor and divide out the common factor.
=
Simplify.
The excluded values are
________ & ________.
Simplify the expressions. State the excluded values.
5x + 10__
3x 2 + 6x
4x 2 + 20x + 25__
4x 2 - 25