SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
Simplifying
Rational
Expressions
April 24, 2013
SWBAT:
𝟕𝒙
Simplify rational expressions and identify excluded values of rational expressions.
𝟏𝒙𝟐
𝟐
or
𝑥2
𝟐
𝟐
𝟓𝒙𝒚
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
Rational expression
A fraction of polynomials where
the denominator does not equal
zero.
Excluded value (undefined)
Any value that makes the
denominator of your original
problem equal to zero.
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
Method: SET only the denominator ≠ 0 and solve.
𝐱+𝟒 ≠𝟎
−4 − 4
𝐱 ≠ −𝟒
−𝟒
𝒙𝟐 − 𝟗 ≠ 𝟎
𝒙𝟐 − 𝟗 ≠ 𝟎
𝒙 −𝟑 𝒙+𝟑 ≠𝟎
𝒙 −𝟑 ≠𝟎 𝒙+𝟑 ≠𝟎
𝒙≠𝟑
−𝟑, 𝟑
𝒙 ≠ −𝟑
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
-24
3 -8
-5
𝒙𝟐 − 𝟓𝐱 − 𝟐𝟒 ≠ 𝟎
𝒙+𝟑 𝒙−𝟖 ≠𝟎
𝒙+𝟑 ≠𝟎 𝒙−𝟖 ≠𝟎
𝒙 ≠ −𝟑
−𝟑, 𝟖
𝒙≠𝟖
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
𝐱+𝟓 ≠𝟎
−𝟓 − 𝟓
𝐱 ≠ −𝟓
−𝟓
𝒙𝟐 − 𝟏𝟔 ≠ 𝟎
𝒙𝟐 − 𝟏𝟔 ≠ 𝟎
𝒙 −𝟒 𝒙+𝟒 ≠𝟎
𝒙 −𝟒 ≠𝟎 𝒙+𝟒 ≠𝟎
𝒙≠𝟒
−𝟒, 𝟒
𝒙 ≠ −𝟒
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
12
4
3
7
𝒙𝟐 + 𝟕𝐱 + 𝟏𝟐 ≠ 𝟎
𝒙+𝟑 𝒙+𝟒 ≠𝟎
𝒙+𝟑 ≠𝟎 𝒙+𝟒 ≠𝟎
𝒙 ≠ −𝟑
−𝟑, −𝟒
𝒙 ≠ −𝟒
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
Reduced Form
denominator
numerator
1
GCF
cancel
common
factors!
SWBAT:
𝟏
Simplify rational expressions and identify excluded values of rational expressions.
𝟐 𝒙−𝟓
𝟒𝒙
𝟐
𝒙−𝟓
𝟐𝒙
𝟑
𝒙−𝟓
𝒙
𝒙−𝟑
𝒙−𝟓
𝒙−𝟑
𝟑
𝟏
𝒙
𝟏
SWBAT:
𝟏𝟎
Simplify rational expressions and identify excluded values of rational expressions.
𝒙−𝟐
𝟏𝟎
𝟑
𝒙−𝟑
𝟑𝒙
𝒙−𝟐
𝒙−𝟑
𝟏
𝒙
𝒙(𝒙 + 𝟔)
𝟓(𝒙 + 𝟔)
𝒙
=
𝟓
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
-5
5
4
-1
𝒙+𝟓
𝟏
𝒙+𝟓 𝒙−𝟏
𝒙−𝟏
1
-1 -1
-2
Diamond!
𝒙−𝟏
𝟏
𝒙−𝟏 𝒙−𝟏
𝒙−𝟏
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
-12
3 -4
-1
4
1
5
4
𝒙+𝟑
𝟏
𝒙+𝟏
𝒙+𝟑 𝒙−𝟒
𝟏
𝒙−𝟒
𝒙+𝟏 𝒙+𝟒
𝒙+𝟒
SWBAT:
𝒙𝟐
Simplify rational expressions and identify excluded values of rational expressions.
− 𝟔𝟒
32
-8 -4
-12
𝒙𝟐 − 𝟐𝟓
𝒙−𝟖 𝒙+𝟖
𝒙−𝟓 𝒙+𝟓
𝒙−𝟖 𝒙−𝟒
𝒙+𝟓 𝒙+𝟓
𝒙+𝟖
=
𝒙−𝟒
𝒙−𝟓
=
𝒙+𝟓
DOTS &
Diamond!
25
5 5
10
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
4
2
4
2
-48
8 -6
2
GCF &
Diamond!
𝒙−𝟐
𝒙+𝟐
𝒙
𝒙+𝟐
𝒙+𝟐
𝒙+𝟖
𝒙−𝟐
=
𝒙+𝟐
𝒙+𝟖
𝒙−𝟔
𝒙
=
𝒙−𝟔
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
“opposites”
=1
= -1
= itself
When factors are both subtraction and
written in the opposite order, they
cancel to equal -1.
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
-1
𝟏𝟔 − 𝒙𝟐
12
-4 -3
-7
𝒙 −4
𝒙−𝟑
𝟒 −x
𝟒+𝒙
−𝟏(𝒙−𝟑)
=
𝟒+𝒙
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
𝟐𝟓 − 𝒙𝟐
10
-5 -2
-7
-1
𝒙− 5
𝒙−𝟐
𝟓 −x
𝟓+𝒙
−𝟏(𝒙−𝟐)
=
𝟓+𝒙
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
SWBAT:
Simplify rational expressions and identify excluded values of rational expressions.
𝐱−𝟑 ≠𝟎
+𝟑 + 𝟑
𝐱 ≠ 𝟑
𝟑
-15
3
-5
-2
(𝒙 − 𝟓)(𝒙 + 𝟑)
𝒙(𝒙 + 𝟑)
𝒙−𝟓
=
𝒙