Rational expressions can be simplified by factoring the numerator and denominator and canceling out common factors. To simplify a rational expression, one should completely factor the numerator and denominator and apply the fundamental principle of rational expressions to eliminate common factors. Only common factors of the numerator and denominator can be canceled out.

1. SIMPLIFYING RATIONAL
EXPRESSIONS

2. RATIONALEXPRESSIONS
Rational expressions can be written in the
form where P and Q are both polynomials
and Q 0.
Examples of Rational
Expressions
P
Q
3x2 2x 4 4x 3y 3x2
4x 5 2x2 3xy 4 y2 4

3. Simplifying Rational Expressions
The process of simplifying numbers
is the same with simplifying rational
expressions.

4. GROUP ACTIVITY
Directions:
Analyze the following numbers whether
a Rational Expression or Rational
Numbers.
You only have 5 minutes for this activity.

5. • 2/-3
• 2x2+7x/x + 1
• -1/5
• 6x/6
• 9x2-1/4x2 + 5
• 25/3x
• 10x2 +4x + 9/ x2 + 4
• 8/5
• 1
• 0
• X2 + 4x + 4/ x2 – 1
• 2x + 10/ x + 5
• 2x + 8/ 3x + 12
• 1/ x
• 2/3

6. Correct Answer
RATIONAL NUMBERS
1.2/-3
2.-1/5
3.8/5
4.2/3
RATIONAL
EXPRESSION
1.2x2+7x/x + 1 2.9x2-
1/4x2 + 5
3.10x2 +4x + 9/ x2 + 4
4.X2 + 4x + 4/ x2 – 1
5.X2 + 4x + 4/ x2 – 1
6.2x + 10/ x + 5
7.2x + 8/ 3x + 12

7. SIMPLIFY:
1. X – 1
5x - 5
Solutions:
= (x – 1)
5( x – 1)
= (x – 1)
5( x – 1)
Final answer:
1
5
STEPS:
1. Look for the GCF or the
common factor of the
numerator and
denominator.
2. Cancel the common
factor.

8. SIMPLIFY THE EXPRESSION
2. xy + 3y
4x + 12
Solution:
= y ( x + 3)
4 ( x + 3)
= y ( x + 3)
4 ( x + 3)
Final Answer:
y
4
Steps:
1. Look for the GCF or the
common factor of the
numerator and
denominator.
2. Cancel the common
factor.

9. YOUR TURN!
GROUP 1:
4b + 8a GROUP 4:
bc + 2ac 2x + 8
3x + 12
GROUP 2:
2xy + 4y2 x2
+ 2xy
GROUP 3:
2x + 10
x + 5

10. Simplifying Rational Expressions
Simplifying a rational expression means writing
it in lowest terms or simplest form.
To do this, we need to use the
Fundamental Principle of Rational Expressions
If P, Q, and R are polynomials, and Q and R are not 0,
PR
QR
P
Q

11. Simplifying a Rational Expression
1) Completely factor the numerator and
denominator.
2) Apply the Fundamental Principle of
Rational Expressions to eliminate common
factors in the numerator and denominator.
Warning!
Only common FACTORS can be eliminated
from the numerator and denominator. Make
sure any expression you eliminate is a
factor.

12. Example 2: Simplifying Rational
Expressions
Simplify each rational expression, if possible. Identify any excluded
values.
4
Factor 14.
Divide out common factors. Note that if
r = 0, the expression is undefined.
Simplify. The excluded value is 0.

13. Example
Simplify the following expression.
7x 35 7(x 5) 7
x2 5x x(x 5) x

14. Example
Simplify the following expression.
x2 3x 4 (x 4)( x 1) x 1
x2 x 20 (x 5)( x 4) x 5

15. Example
Simplify the following expression.
7
y
y
7
1(
y
y
7
7)
1

16. Simplify each expression.
1. 2.
Factor each expression.
3. x2 + 5x + 6 4. 4x2 – 64
(x + 2)(x + 3)
5. 2x2 + 3x + 1
(2x + 1)(x + 1)
4(x + 4)(x – 4)
6. 9x2 + 60x + 100
(3x +10)2

17. GENERALIZATION
What is Rational
Expression?
What is Rational
Numbers?
What are the steps in
simplifying rational
expression?

18. INDIVIDUAL SEATWORK
• Get ½ crosswise.
Direction: Simplify the
following expression
1. 5x2 + 20
2x + 8
2. 21xy + 6y2
42x + 12y
3.2x2 + 2x
3x2 + 3x
4. x – 1
x2 – 1
5. p2 – p -6
p - 3

19. CORRECT ANSWER
1.5 /2
2.3y/6 or y/2
3.2x/3x
4.1/x + 1
5. p + 2/ 1

20. CORRECT ANSWER
1.5 /2
2.3y/6 or y/2
3.2x/3x
4.1/x + 1
5. p + 2/ 1