Page 258 - Algebra 1

L E S S O N Using the Distributive Property to Simplify
39
Rational Expressions
Warm Up
1. Vocabulary The set of __________ numbers includes all rational and
(1)
Simplify.
2. -3x2y (4x2y-1 - xy)
(15)
3. m_n(2x - 3my + 5ny) (15)
4. 5x-25x2 (38) 5x
5. Factor. 3a2b3 - 6a4b + 12ab (38)
A rational expression is an expression with a variable in the denominator. Rational expressions can be treated just like fractions. As with fractions, the denominator cannot equal zero. Therefore, any value of the variable that makes the denominator equal to zero is not permitted.
Variables stand for unknown real numbers. So, all properties that apply to real numbers also apply to rational expressions. The Distributive Property can be used to simplify rational expressions.
Distributing Over Addition
irrational numbers.
New Concepts
Math Reasoning
Write Why isn’t division by zero allowed?
Example
1
x2(x2 3y ) _ _ _3
x2 (x2 3y ) __ _3
Simplify y2 y + m . SOLUTION
y2 y+m
Hint
When multiplying powers, add the exponents. When dividing powers, subtract the exponents.
x2x2 x23y x2 __ __3 _
=(2 · y)+(2 · m ) Multiply y2 byeachterminsidetheparentheses. yy
x4 3x y _ _2 3
= y3 + y2m
Simplify.
Note that y ≠ 0 and m ≠ 0 because either value would make the denominator equal to zero.
x4 3x y _ _2
y3 + m ;y≠0,m≠0
Online Connection www.SaxonMathResources.com
Lesson 39 243