A rational algebraic expression is defined as a polynomial divided by another polynomial. The document outlines the steps to simplify such expressions, including factoring, dividing out common factors, and multiplying the remaining factors. It also provides examples and activities for practicing simplification.

1. SIMPLIFYING RATIONAL
ALGEBRAIC EXPRESSION
MATHEMATICS 8

2. WHAT IS A RATIONAL ALGEBRAIC
EXPRESSION?
Rational algebraic expression is a
polynomial divided by another
polynomial, such as (x+1)/(2x+3) or
𝑥+1
2𝑥+3
.
Is
28𝑥3
7𝑥4 a rational expression?

3. IN OR OUT
1.
8𝑏2
4𝑎𝑏
6.
𝑥2
𝑥
2.
𝑥+4
4+𝑥
7.
−𝑥(𝑥+4)2
𝑥−4
3.
2𝑥+4
𝑥+2
8.
𝑥+2
2𝑥+2
4. 21 9.
3𝑥−12
5𝑥−20
5.
21
𝑥
10.
45𝑎𝑏
30𝑎𝑏

4. HOW TO SIMPLIFY RATIONAL
ALGEBRAIC EXPRESSION
In simplifying Rational Algebraic Expression. There
are three steps that we need to consider.
1. Factor completely the numerator and
denominator.
2. Separate and divide out common factor/s if there
is/are any.
3. Multiply the remaining factors.

5. EXAMPLE 1
Write the rational expression
28𝑥3
7𝑥4 in simplest form.
Step 1.
28𝑥3
7𝑥4 =
4(7𝑥3)
𝑥(7𝑥3)
(Factor completely the numerator and denominator)
Step 2.
Separate
4
𝑥
from
7𝑥3
7𝑥3 to get
4
𝑥
x
7𝑥3
7𝑥3
Step 3
Simplify the equation and we will get
4
𝑥
x1
=
4
𝑥

6. EXAMPLE 2
Write the rational expression in
3𝑥−12
5𝑥−20
in simplest form.
Step 1.
3𝑥−12
5𝑥−20
=
3
5
x
𝑥−4
𝑥−4
Step 2.
3
5
x
𝑥−4
𝑥−4
=
3
5
x1
Step 3.
We multiply the remaining factors
3
5
x1 to get the final answer
3
5
.
=
3
5

7. GROUP ACTIVITY
Group 1
𝑥2−3𝑥−10
𝑥2−7𝑥+10
𝑥2+5𝑥+4
𝑥+4
Group 2
𝑥+2
2𝑥+2
𝑥2−5𝑥+6
𝑥−3

8. INDIVIDUAL ACTIVITY
Simplify the following Rational Algebraic
Expression
1.
𝑥2−16
𝑥2+9𝑥+20
4.
𝑥2−4𝑥+4
𝑥2−5𝑥+6
2.
𝑥+5
𝑥2−25
5.
3𝑥2−6𝑥
2𝑥−4
3.
3𝑥−9
𝑥2−4𝑥+3

9. ASSIGNMENT
For your assignment simplify the following
expressions.
1.
8𝑏2
4𝑎𝑏
2.
𝑥+4
4+𝑥
3.
2𝑥+4
𝑥+2