Rational Functions w/ Teacher Ian

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Concept of

Rational
Functions

▪ Real-life situations using Rational Function

▪ Rational Function, Rational Equation and Rational Inequality

STEP 4:

CHECKING

Substitute the value of x to the original equation

Therefore, -4 is the solution

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In the previous lesson, we have learned the concept of
a function. In this lesson, we will learn a function in
the form of a fraction called rational function.

Rational functions are used in various areas of study
like creating a model of average cost functions, precise
ratio of materials in constructing architectural designs,
and in business and economics to help make a right
decision, planning, and predicting outcomes of events.
A correct formula of rational functions provides a better
understanding to achieve the desired outcomes.

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Recall:

▪ How do we add and subtract similar fraction?

▪ How do we add and subtract dissimilar fractions?

▪ How do we solve for the product and quotient of
fractions?

▪ What is rational expression?

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▪ How do we add and subtract

similar fractions?

In adding and subtracting
similar fractions, just copy
the denominator and add
or subtract the numerator.

ADDITION OF SIMILAR FRACTION
SUBTRACTION OF SIMILAR

FRACTION

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In adding and subtracting
dissimilar fractions, find

the least common

denominator or LCD of the

given fractions.

▪ How do we add and subtract

dissimilar fractions?

ADDITION OF DISSIMILAR FRACTION

SUBTRACTION OF DISSIMILAR

FRACTION

÷

x

=

÷

x

=

x 1

x 2

x 3

x 4

8

16

24

32

6

12

18

24

To find the LCD, list the

multiples of 6 and 8

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To solve for the product of

two fractions, multiply
numerator by numerator

and denominator by

denominator.

▪ How do we solve for the product

and Quotient of Fraction

2.

1.

Reciprocate the

divisor then
proceed to

multiplication

To solve for the
quotient of two
fractions, take
the reciprocal
of the divisor

then proceed to
multiplication.

SOLVING RATIONAL

EQUATION

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What is Rational

Expression?

❑ A rational expression is an expression that can be

written as a ratio of two polynomials.

❑

A rational expression can be described as a function
where either the numerator, denominator or both
have a variable on it.

❖ STEPS IN SOLVING RATIONAL EQUATION

1.

Determine the LCD

2.

Multiply both sides of the equations by LCD

3.

Solve the resulting equation

4.

Check for the apparent solution

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Real Life Situations
Using Rational Function

EXAMPLE NO 1:

Solution:

STEP 1:

=

STEP 4: CHECKING
The LCD of all denominators is 4

STEP 2:

Multiply both sides of the equation by 4

STEP 3:

Solve the resulting equation

=

Substitute the value of x
to the original equation

Therefore, 3 is the solution

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Which one do you prefer: working alone or working with others? Do
you know that dividing task and other real-life situations can be
represented as rational function?

STEPS IN SOLVING PROBLEMS INVOLVING WORK

STEP 1

STEP 2

STEP 3

Solve the equation created in the first step. This can
be done by first multiplying the entire problem by the
common denominator and then solving the resulting
equation.

Answer the question asked of you in the problem and
be sure to include units with your answer.

NOTE: WHEN EACH SIDE OF THE EQUATION IS A SINGLE
RATIONAL

EXPRESSION,

WE

CAN

ALSO

USE

CROSS

MULTIPLICATION

3 (4) = x (4)

12

=

4x

=

=

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Example No. 1

Cesar and Kyla are asked to paint a house. Cesar can paint the house by
himself in 12 hours and Kyla can paint the house by herself in 16 hours.
How long would it take to paint the house if they worked together?

Substitute the given to the formula:

Given:

T = ?
A (Cesar) = 12 hours
B (Kyla) = 16 hours

In this case the least common denominator or LCD is 48.
Multiply 48 to both sides of equation

SOLUTION

Step 1:

Step 2:

Step 3:

x1

x2

x3

x4

x5

12

24

36

48

60

16

32

48

64

80

EXAMPLE NO 2:

Solution:

STEP 1:

-

The LCD of all denominators is 6

STEP 2:

Multiply both sides of the equation by 6

STEP 3:

Solve the resulting equation

-

=

=

=

=

2 + 3

=

5

x1

x2

x3

6

12

18

2

4

6

3

6

9

STEP 4:

CHECKING

Substitute the value of x to the original equation

Therefore, 1 is the solution

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Example No. 2

Assume that the two persons doing the same work. Kaye can finish her
work for two hours and Aaron can finish his work in 4 hours. How long it
would take if they would work together?

Substitute the given to the formula:

Given:

T = ?
A (Kaye) = 2 hours
B (Aaron)= 4 hours

In this case the least common denominator or LCD is 4.
Multiply 4 to both sides of equation

“Two heads are better than one”. If

you will work as a team, you can

finish the job faster.

SOLUTION

Step 1:

Step 2:

Step 3:

EXAMPLE NO 3:

Solution:

STEP 1:

-

The LCD of all denominators is 10x

STEP 2:

Multiply both sides of the equation by 10x

STEP 3:

Solve the resulting equation

-

=

=

=

STEP 4:

CHECKING

Substitute the value of x to the original equation

Therefore, 5 is the solution

=

=

=

=

EXAMPLE NO 4:

Solution:

STEP 1:

STEP 2:

STEP 3:

Solve the resulting equation

=

=

=

STEP 4:

CHECKING

Substitute the value of x to the original equation

Therefore, -4 is the solution