Solving Rational Equations and Inequalities
pg. 1
Name: _______________________________________________________________________
x
1

Solve
.
x6 x4
 There are two methods for solving rational functions using a graphing calculator.
 Method 1: Using the Intersection
i. For this method, separate the function into two separate functions.
ii. Press Y= on the calculator and enter the first function into Y1 and the second
into Y2. Be sure to follow the order of operations.
iii. Press GRAPH. Try to locate the intersection of the two curves. You will
want to adjust your window settings to 1.5 ≤ x ≤ 3.5 and -1.3 ≤ y ≤ -0.1 to see
these points clearly.
iv. Press CALC then choose 5: intersect. Follow the directions the calculator
gives you.
1. What are the points of intersections of this graph?
2. What do the x-values of these points tell us?

Method 2: Using the Zeros
i. For this method, subtract one side of the function from the other to get an
expression that will be equal to zero.
ii. Press Y= and clear the previous equations. Enter your new function into Y1.
Be sure to follow the order of operations.
iii. Press GRAPH. Locate where the curve crosses the x-axis. You will want to
reset your window settings to -2 ≤ x ≤ 4 and -0.5 ≤ y ≤ 0.5.
iv. Press CALC then choose 2: zero. Follow the directions the calculator gives
you.
3. For what x-values is the graph of the function zero?
4. What do these zeros mean?
5. How do the zeros compare to the intersections from Method 1?

Now solve the equation algebraically.
6. How do these solutions compare to your solutions from the graphing calculator?
Solve
x
2x
18

 2
. Group A use Method 1 and Group B use Method 2.
x3 x3 x 9
7. Where are the zeros of this graph?

Now solve the equation algebraically.
8. How do these solutions compare to your solutions from the graphing calculator?
Solving Rational Equations and Inequalities
Solve
pg. 2
x2
x
. Group A use Method 2 and Group B use Method 1.

2( x  3) x  3
9. Where are the zeros of this graph?

Now solve the equation algebraically.
10. How do these solutions compare to your solutions from the graphing calculator?
Solve
x
 1.
2x  1
 The steps for solving rational inequalities using a graphing calculator are very
similar to the intersection method.
i. Enter one function into Y1 and the other into Y2.
ii. Press GRAPH and answer the following questions.
11. How can we look at the graph to determine where the solutions are?
12. What are the solutions to the inequality?

Now solve the inequality algebraically.
13. How do these solutions compare to your solutions from the graphing calculator?
Solve
2x  1
 4.
x2
14. What are the solutions to the inequality?

Now solve the inequality algebraically.
15. How do these solutions compare to your solutions from the graphing calculator?
Solve
7x
 2.
3x  2
16. How does the sign change the method for solving this inequality?
17. What are the solutions to the inequality?

Now solve the inequality algebraically.
18. How do these solutions compare to your solutions from the graphing calculator?