9.6 Solving Rational Equations and Inequalities
Warm-up: Simplify each expression.
a.
b.
1
Rational Equations
Example 1: Solve and check.
a.
b. You try
2
c.
3
e. You try
4
f.
5
Rational Inequalities
Steps for Solving Rational Inequalities:
1. State excluded values. (these are values that would make any of
your denominators 0)
2. Solve. (the same way you would solve a rational equation)
3. Test. (Divide a number line into regions separated by your excluded
values and the answer(s) you got in step 2. Test values in each region
to determine which interval(s) satisfy the inequality.)
6
Example 2: Solve.
a.
7
b.
8
Real-World Applications:
Example 3: Every year, the junior and senior classes at Hillcrest High
School build a house for the community. If it takes the senior class 24
days to complete a house and 18 days if they work with the junior
class, how long would it take the junior class to complete a house if
they worked alone?
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Example 4: Sandra is rowing a canoe on Stanhope Lake. Her rate in
still water is 6 miles per hour. It takes Sandra 3 hours to travel 10
miles round trip. Assuming that Sandra rowed at a constant rate of
speed, determine the rate of the current.
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