9.6 Solving Rational Equations and Inequalities
Rational Equations
9.6 Solving Rational Equations and Inequalities
Warm­up: Simplify each expression.
Example 1: Solve and check.
a.
a.
b.
b. You try
e. You try
c.
d. You try
f.
Rational Inequalities
Example 2: Solve.
Steps for Solving Rational Inequalities:
a.
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.) 1
9.6 Solving Rational Equations and Inequalities
c. You try
b.
Real­World 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?
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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