I.
OBJECTIVES
At the end of this class the students shall be able to:
Define the word “rational” and rational equation
Solve the rational equation
Apply the rational expression in real life situation
II. SUBJECT MATTER
A. TOPIC: RATIONAL Algebraic equation
B. MATERIALS: CARTOLINA, MARKER, CHALK AND BLACKBOARD
C. REFERENCE: Agner Sergio. (October 7, 2021) Rational expressions and equations.pdf
retrieved from https//www.scribd.com/pdf/Gen-math11-solving-rational-equations-080820
III. PROCEDURE
TEACHER’S ACTIVITY STUDENT’S ACTIVITY
A. ENGAGEMENT
Good morning class! Good morning, ma’am.
Everybody, please stand up and let us pray first.
Kindly arrange your chair in the proper position before you take your
sit. Thank you, ma’am.
You may now take your sit.
Last meeting, what did we discussed? About the algebraic expression
What is an algebraic expression? Algebraic expression is an expression built up with constant
algebraic numbers and variables.
Very good!
B. EXPLORATION
Now, lets have an activity first before we proceed to our new topic.
I will group you into four groups, I have an equation and you are
going to give me the simplest form or the expanded form of the
given eauation. The group that will have the first 3 points will win.
1. x+4x
2. 2x-x
3. x+y Answers
4. 3(x+1) 1. 5x
5. -2x+6x 2. x
6. 2a-2a² 3. x+y
7. 4x-12 4. 3x+3
8. x²+2x+1 5.4x
9. (x+y)² 6. 2a(1-a)
10. x²-2xy+y² 7. 4(x-3)
8. (x+1)²
9. x²+2xy+y²
Very good class, thank you for your participation. Now 10. (x-y)²
what did you observe with our activity?
Okay, very good observation. Now that you already know how to Simplifying and operation of algebraic equation.
simplify polynomials, let us know the rational expression and
equation. From the root word of rational, “ratio”, what is rational?
Very good.
Ratio means comparing two data using a division. And rational is a
comparing of two polynomials using division.
C. EXPLANATION
Now let’s have a better understanding of rational expressions and
equations.
Let’s have an example of rational expression.
1
1.
x
x+1
2.
x
These two are examples of rational expression.
Let’s have another example involving the simplifying of rational
expression.
x 1
1. = , since we can cancel out the variable “x” so we can
3x 3
simplify the expression as 1/3.
y ² ( y )( y ) y
2. = ¿ ,
2 y 2( y) 2
2x+4
3. , factor out the 2 since it is also factorable to 4, so it will
x +2
2(x+ 2)
become and then now, since x+2 divided by itself is 1 so
x +2
the simplest form is 2.
x ²+ 2 x +1
4. , the factor of the numerator is x+1 and x+1, we
x+ 1
( x +1)(x+1)
can write it like this then the simplest form will
x +1
be x+1. Rational expression is written as a quotient of two polynomials,
where the denominator should not be equal to zero.
4 x−6 x ²
5. let’s find the expanded form of numerator, so it will
2−3 x
2 x (2−3 x )
become and then 2x-3 divided by itself is 1 so the
2−3 x 2 x
+ =4
simplest form is 2x. x 2
Based on my given examples, what is a rational expression?
It is an equation that contains rational expressions.
Now, 2x+1=3 is an example of equation. When we say rational
equation, who can give me an example of rational equation?
So, what is a rational equation?
Very good!
A rational equation is an equation containing at least one rational
expression. Let’s have an example,
5 3 x 9 x
1. − = 4. =
8 5 10 x 4
8 x+2 x +9
2. x + =6 5. +4=
x 3 2
x+ 3 12
3. =
x−3 3
Now let’s know how to solve a rational equation. Let’s use the given
examples.
5 3 x
1. − =
8 5 10
Step 1, determine the LCD.
LCM= 40
Step 2, Multiply both sides of the equation by the LCM.
5 3 x
( − = )40
8 5 10
Step 3. Simplify.
1
25-24 = 4x , 1 = 4x, thus =x
4
8
2. x + =6
x
8
x + =6
x
( x + 8x =6) x
x²+8 = 6x
x²-6x+8 = 0
(x-4) (x-2) =0
x-4=0, thus x=4
x-2=0, thus x=2
x+ 3 12
3. = Use the cross multiplication
x−3 3
Yes ma’am.
12x-36 = 3x+9
12x-3x = 9+36
9x = 45, thus x = 5
9 x
4. =
x 4
x² = 36 √ x ² = √ 36
x=6
x+2 x +9
5. +4= LCM = 6
3 2
¿)6
2x + 4 + 24 = 3x + 27
2x + 28 = 3x + 27
2x – 3x = 27 – 28
-x = -1, x = 1
Did you understand, class?
Very good.
D. ELABORATION
Now, I will call five students to answer on the board. Rechelle,
Marygrace, Rodel, Cristina and Jomelyn.
2 3 1
1. − =
x 2x 5 Solutions
2 3 1
1. ( − = ) 10x
x 2x 5
20 x 30 x 10 x
− =
3 2 x 2x 5¿
2. = ¿
x+1 x−3 20 – 15 = 2x
5 = 2x, x = 5/2
3 2
2. =
x+1 x−3
2(x+1) = 3 (x-3)
2x + 2 = 3x – 9
2 2x -3x = -9-2
3.
x −4 x = 14−9 x
x−2 x−2 -x = -11
x = 11
2
x −4 x = 14−9 x )
3. ( x−2
x−2 x−2
2
x −4 x=14−9 x
2
x + 9 x−4 x −14=0
4 8 2
x + 5 x −14=0
4. + =4
x x+ 2
(x + 7) (x – 2) = 0
x = -7, x = 2
4 8
4. ( + =4 ¿ x (x+2)
x x+ 2
4x + 8 + 8x = 4x(x+2)
12x + 8 = 4x² + 8x
0 = 4x² + 8x -12x -8
0= 4x²- 4x – 8
0 = 4 ( x² - x -2)
x 5 14 0 = 4 (x-2)(x+1)
5. − =
x+5 x−5 (x +5)(x−5)
X = 2, x=-1
x 5 14
5. { − = } ( x +5 ) ( x−5 )
x+5 x−5 ( x +5 ) ( x −5 )
x(x-5) – 5(x+5) = 14
x² -5x -5x -25 =14
x²- 10x -25 – 14 = 0
x²- 10x -39 =0
Very good class!
(x-13) (x+3) = 0
It seems that you understand now how to solve a rational equation.
So, in solving the rational equations, what are the procedure to solve X= 13, x= -3
it.
Very good!
When it comes to real life situation, how can we apply rational
expression? Find the least common multiple or the least common denominator.
And the simplify the reluctance equation to get the final answer.
Very good! Rational equations can be used to solve a variety of problems that
involve rates, times, and work. Using rational expressions and
equations can help you answer questions about how to combine
workers or machines to complete a job on schedule.
E. EVALUATION
Solve each equation.
3 x
1. =
x 12
x+ 3 15
2. =
x−3 17
x−3 x
3. + =2 x
5 7
2x x 3
4. − =
x−1 x +1 x2 −1
3x 5
5. − =x ²
2 2x
IV. ASSISNMENT
Have an advance study about rational inequalities. Write down 5 examples in a ½ sheet of paper.
