Transcript Document

Objectives:
Be able to solve various rational equations and
exclude any extraneous solutions.
Critical Vocabulary:
Rational Function, Extraneous solution
II. Solving Rational Equations
a. Solving a Rational: Cross Multiplication (Proportion)
1.
6t  7 3t  8 First determine

4t  1 2t  4 what “x” can’t be
1
x  ,2
4
(6t + 7)(2t - 4) = (4t - 1)(3t + 8)
Cross Multiply
12t2 - 10t - 28 = 12t2 + 29t - 8
FOIL
-10t - 28 = 29t - 8
-39t - 28 = -8
-39t = 20
What are talking about?
What is an extraneous
solution?
Solution: x = -20/39
That’s
Look like
where
you your
didn’tsolution
get any
is one
extraneous
of the values
solutions.
that “x”
can’t be.
II. Solving Rational Equations
b. Solving a Rational: By Finding LCM (Denominator)
3
7
2.
4
x
2x
What can x not be?
x0
7 
3
2 x  4 

2x 
x
Multiply by LCD
Distribute
6 + 8x = 7
8x = 1
Solution: x = 1/8
No….really?
This is not an
extraneous
solution either.
II. Solving Rational Equations
3x
3
3.
2
x 1
x 1
3 
 3x
x  1
2

x 1 
 x 1
3x + 2(x - 1) = 3
3x + 2x - 2 = 3
5x - 2 = 3
5x = 5
x=1
Solution: None
What can x not be?
x 1
Multiply by LCD
Distribute
This means
there is no
solution
This is
extraneous.
What does
that mean?
II. Solving Rational Equations
2x
4
1
4. 2
 2

Factor Denominators
x 4 x 4 x2
2x
4
1


x  2,2
( x  2)(x  2) ( x  2)(x  2) x  2

2x
4
1 

( x  2)(x  2)


 ( x  2)(x  2) ( x  2)(x  2) x  2 
2x = 4 - (x - 2)
2x = 4 - x + 2
3x = 6
x=2
Solution: None