simplifying RAE

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

2. 1. illustrate rational algebraic
expressions; and
2. simplify rational algebraic
expressions.

3. RATIONAL ALGEBRAIC EXPRESSIONS
- A rational expression in one variable is
an expression that can be written in the
form
𝑷
𝑸
, where P and Q are polynomials.
𝟒
𝒙 −𝟐
𝒙𝟐
+ 𝟐𝒙 − 𝟑𝟓
𝟑𝒙 + 𝟒
𝟒𝒙
𝒙𝟐 + 𝟗
not UNDEFINED
Remember, Q ≠ 0,

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

5. UNDEFINED
To make a rational expression
𝒙𝟐−𝟐
𝒙 −𝟒
UNDEFINED,
x – 4 = 0
equate 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
𝟐𝒙
(𝒙𝟐+𝟓𝒙+𝟔)
UNDEFINED
𝒙𝟐
+ 𝟓𝒙 + 𝟔
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
𝟐𝒙
(𝒙𝟐−𝟗)
UNDEFINED,
𝒙𝟐
− 9 = 0
equate 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:
𝟔𝒙+𝟏𝟐
𝟑
=
𝟑(𝟐𝒙+𝟔)
𝟑
Cancel out or divide
the common factor. =
𝟑(𝟐𝒙+𝟔)
𝟑
Simplify. = 2x + 6
GCF: 3

9. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
𝒙𝟐−𝟔𝒙+𝟖
𝟒𝒙−𝟖
=
(𝒙−𝟒)(𝒙−𝟐)
𝟒(𝒙−𝟐)
Cancel out or divide
the common factor.
=
(𝒙−𝟒)(𝒙−𝟐)
𝟒(𝒙−𝟐)
Simplify. =
(𝒙−𝟒)
𝟒
GCF: 4

10. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
𝒂𝟐+𝒂−𝟔
𝒂𝟐−𝟐𝒂−𝟏𝟓
=
(𝒂+𝟑)(𝒂−𝟐)
(𝒂−𝟓)(𝒂+𝟑)
Cancel out or divide
the common factor.
=
(𝒂+𝟑)(𝒂−𝟐)
(𝒂−𝟓)(𝒂+𝟑)
Simplify. =
(𝒂−𝟐)
(𝒂−𝟓)

11. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
𝟑𝒙𝟐𝒚𝟒
𝟗𝒙𝟑𝒚𝟐
=
𝟑·𝒙𝟐·𝒚𝟐·𝒚𝟐
𝟗·𝒙𝟐·𝒙·𝒚𝟐
Cancel out or divide
the common factor.
=
𝟑·𝒙𝟐·𝒚𝟐·𝒚𝟐
𝟗·𝒙𝟐·𝒙·𝒚𝟐
Simplify. =
𝒚𝟐
𝟑𝒙

12. SIMPLIFYING RATIONAL ALGEBRAIC
EXPRESSIONS
Factor the numerator
and denominator
Example:
𝟏𝟐𝒙𝟓𝒚𝟒
𝟐𝒙𝟑𝒚𝟕
=
𝟏𝟐·𝒙𝟑·𝒙𝟐·𝒚𝟒
𝟐·𝒙𝟑·𝒚𝟒·𝒚𝟑
Cancel out or divide
the common factor.
=
𝟏𝟐·𝒙𝟑·𝒙𝟐·𝒚𝟒
𝟐·𝒙𝟑·𝒚𝟒·𝒚𝟑
Simplify. =
𝟔𝒙𝟐
𝒚𝟑