Algebra 1
Name: _______________________________
Unit 7: Lesson 4
Date: _________________ Period: _______
Simplifying Rational Expressions (11.4)
Essential Questions:
 What is required to simplify fractions?
 When is an expression simplified?
Goal: I can simplify rational expressions by factoring.
Key Ideas / Vocabulary:
 Rational Expression: an expression that can be written in the form A/B where A and B are polynomials
and the value of B is not _____________ .
Steps / Procedure:
1) _______________ the numerator(s) and denominator(s) completely!
2) Find the __________________ ________________. What number(s) make the denominator equal to
___________ or undefined?
3) Cancel out any factors that are _______________ to both the numerator(s) and denominator(s).
Factoring Review:
Binomials
1) GCF
2)
Trinomials
1) GCF
2)
4-Terms
1) GCF
2)
Section 1: READY… Simplify the rational expression in factored form. State the excluded values.
1)
5y3
10 y 2 ( y  2)
YT 1)
3 x ( x  7)
15 x 2
2)
 ( x  6)
( x  6)
YT 2)
( x  1)( x  5)
( x  1)( x  5)
3)
x9
x
YT 3)
y ( y  3)( y  2)
( y  2)( y  3)
Section 2: NOT READY… Simplify the rational expression (factor completely first!) State the excluded values.
x3  4 x 2
4)
3x 2  12 x
2r 2  4r
YT 4)
8r  16
5)
v5
v  10v  25
YT 5)
x6
x  5x  6
6)
y 2  8 y  12
y 2  3 y  18
YT 6)
a 2  11a  18
a 2  2a  8
7)
2 z 2  72
4 z 2  28 z  24
YT 7)
b 2  3b  28
b 2  49
2
2
Section 3: UNDEFINED… For what values of the variable is the rational expression undefined.
8)
c9
c  c  12
YT 8)
2
3
d  36
2
Section 4: Keystone Application.
9) What is the ratio of the area of
the smaller rectangle to the area
of the larger rectangle?
Homework:
YT 9) What is the ratio of the area of the smaller
rectangle to the area of the larger rectangle?
“Rational Expressions” Packet # 51-70 All
Ticket Out / Lesson summary: Explain and correct the mistake in simplifying
3x  5
as 3x  1 .
5