This document provides instruction on rational algebraic expressions including: 1) How to illustrate, evaluate, and find values that make rational expressions undefined. 2) Examples of evaluating expressions at given values of variables and finding values that make expressions undefined. 3) A test with problems evaluating rational expressions and finding undefined values.

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

2. 1. illustrate rational algebraic
expressions;
2. evaluate rational algebraic
expressions, and
3. find every value of the variables
that makes a rational expression
undefined.

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. EVALUATING ALGEBRAIC EXPRESSIONS
Evaluate the expression
𝒙𝟐− 𝟒
𝒙 −𝟐
when…
=
𝒙𝟐− 𝟒
𝒙 −𝟐
x = 0
=
( )𝟐− 𝟒
( ) −𝟐
0
0
=
− 𝟒
−𝟐
= 2
=
𝒙𝟐− 𝟒
𝒙 −𝟐
x = 1
=
( )𝟐− 𝟒
( ) −𝟐
=
− 𝟑
−𝟏
= 3
1
1
=
𝟏− 𝟒
𝟏−𝟐

5. EVALUATING ALGEBRAIC EXPRESSIONS
Evaluate the expression
𝒙𝟐−𝟐
𝒙 −𝟒
when…
=
𝒙𝟐−𝟐
𝒙 −𝟒
x = 1
=
( )𝟐−𝟐
− 𝟒
1
1
=
𝟏−𝟐
𝟏−𝟒
=
𝟏
𝟑
=
𝒙𝟐− 𝟒
𝒙 −𝟐
x = 2
=
( )𝟐−𝟐
−𝟒
=
𝟐
−𝟐
= -1
2
2
=
𝟒 −𝟐
𝟐 − 𝟒
=
−𝟏
−𝟑

6. EVALUATING ALGEBRAIC EXPRESSIONS
Evaluate the expression
𝒂𝟐−𝟐𝒃
𝒂 −𝒃
when…
=
𝒂𝟐−𝟐𝒃
𝒂 −𝒃
a = 1 b = 2
=
( )𝟐−𝟐( )
−( )
1
1
=
𝟏−𝟒
𝟏−𝟐
= 3
=
−𝟑
−𝟏
2
2
=
𝒂𝟐−𝟐𝒃
𝒂 −𝒃
a = 2 b = 3
=
( )𝟐−𝟐( )
−( )
2
2
=
𝟒−𝟔
𝟐−𝟑
= 2
=
−𝟐
−𝟏
3
3

7. 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
The expression
𝒙𝟐−𝟐
𝒙 −𝟒
is UNDEFINED if x is replaced by
4, because the denominator would be 0.

8. UNDEFINED
To make a rational expression
𝒙𝟐−𝟒
𝒙 −𝟐
UNDEFINED,
x – 2 = 0
equate the denominator to zero
solve for the variable x = 0 + 2
x = 2
The expression
𝒙𝟐−𝟒
𝒙 −𝟐
is UNDEFINED if x is replaced by
2, because the denominator would be 0.

9. UNDEFINED
To make a rational expression
𝒙𝟐−𝒚
𝒙 −𝒚
UNDEFINED,
x – y = 0
equate the denominator to zero
solve for the variable x = 0 + y
x = y
The expression
𝒙𝟐−𝒚
𝒙 −𝒚
is UNDEFINED if the variables
x and y are replaced by equal values.

10. Test Yourself.
1. Explain how to evaluate an algebraic
expression.
2. What causes a rational expression to
be undefined?
3. How do you find the values that may
cause a rational expression to be
undefined?

11. Test Yourself.
I. Evaluate each rational expression if a = 1
and b = 2
1.
𝑎
𝑏2 2.
2𝑎−𝑏
3𝑎𝑏
II. Find the value of the variable that makes
the expression undefined.
1.
3𝑎
4𝑏
2.
2𝑎−𝑏
𝑏−3