Simplifying Rational Algebraic Expressions

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1. Grade 8 –Mathematics
Quarter I
SIMPLIFYING RATIONAL
ALGEBRAIC EXPRESSIONS

2. 1.illustraterationalalgebraic
expressions;and
2.simplifyrationalalgebraic
expressions.

3. RATIONAL ALGEBRAIC EXPRESSIONS
-A rational expression in one variable is
an expression that can be written in the
form
�
�
, where Pand Qare polynomials.
�
�−�
�
�
+��−��
��+�
��
�
�
+�
not UNDEFINEDRemember, Q ≠0,

4. DOMAIN
-is the set of all possible values of the
variable that are allowed.
-restricted valuescan make a rational
expression undefined.

5. UNDEFINED
To make a rational expression
�
�
−�
�−�
UNDEFINED,
x –4 = 0equate the denominator to zero
solve for the variable x = 0 + 4
x = 4
Domain: All real numbers except 4.

6. UNDEFINED
To make a rational expression
��
(�
�
+��+�)
UNDEFINED,
�
�
+��+�
equate the denominator to zero
solve for the variable
Domain: All real numbers except -2 and -3.
(x + 2)(x + 3)= 0
x + 2 = 0 x + 3 = 0
x = -2 x = -3

7. UNDEFINED
To make a rational expression
��
(�
�
−�)
UNDEFINED,
�
�
−9= 0equate the denominator to zero
solve for the variable
x + 9 = 0
Domain: All real numbers except -9 and 9.
(x + 9)(x -9)= 0
x -9 = 0
x = -9 x = 9

8. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
��+��
�
=
�(��+�)
�
Cancel out or divide
the common factor. =
�(��+�)
�
Simplify. =2x + 6
GCF: 3

9. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
�
�
−��+�
��−�
=
(�−�)(�−�)
�(�−�)
Cancel out or divide
the common factor.
=
(�−�)(�−�)
�(�−�)
Simplify. =
(�−�)
�
GCF: 4

10. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
??????
�
+??????−�
??????
�
−�??????−��
=
(??????+�)(??????−�)
(??????−�)(??????+�)
Cancel out or divide
the common factor.
=
(??????+�)(??????−�)
(??????−�)(??????+�)
Simplify. =
(??????−�)
(??????−�)

11. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
��
�
�
�
��
�
�
�
=
�·�
�
·�
�
·�
�
�·�
�
·�·�
�
Cancel out or divide
the common factor.
=
�·�
�
·�
�
·�
�
�·�
�
·�·�
�
Simplify. =
�
�
��

12. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
���
�
�
�
��
�
�
�
=
��·�
�
·�
�
·�
�
�·�
�
·�
�
·�
�
Cancel out or divide
the common factor.
=
��·�
�
·�
�
·�
�
�·�
�
·�
�
·�
�
Simplify. =
��
�
�
�