Warm Up:
Identify all asymptotes and the
domain of the function
2x
y
x4
3x  2
y
x2
5x2  4
y
x2
Warm Up:
Identify all asymptotes and the
domain of the function
2x
y
x4
3x  2
y
x2
5x2  4
y
x2
Objective

The students will solve rational equations
Recall: Simplify the rational
expressions

2 3
1.  
3 5
1
2. 2 x  3 
2
2
3.
 
x  2 x
Our goal was to match
denominators, and combine
numerators.
Notes

What if you have a
rational EQUATION?
2
35
x
Checking for Solutions
Graphically

Intersection Method





2
35
x
Y1=left side
Y2=right side
Their intersection(s) is(are) the solution(s)
OR
Set the equation = 0 and look for the xintercepts on the graph
I tend to have more luck with the second
approach just because it is easier to scan the x
axis than it is to zoom in, zoom out, change
window and search for a potential intersection.
Intersection Method
2
35
x
Other Method
2
35
x
Checking for Solutions
Algebraically



Your goal is to force match the denominators
Then pull numerators and solve resulting
equation
Check for extraneous solutions


Substitute back into ORIGINAL equation
Result of issues with domain
The Solution is an Extraneous Solution
Extraneous Solution: Solution to
equation that does not satisfy the
original equation.
Example 1
2 3
  2
3 x
Example 2
1
3
6x

 2
x2 x2
x 4
On Your Own

1
3
5

 2
x  2 x  7 x  9 x  14
On Your Own
5
3
10

 2
x  5 x  5 x  25
Assessment
 Bonus…The
 Class
Challenge
Practice: Page 303
#34-44 evens
 Closure
The Challenge
2
1
6 x  5x  1  0
Closure
