March 05, 2013
AA
9 - 6 Solving Rational Equations &
Inequalities
Rational Equation:
* Any equation that contains one or more
rational expressions.
Example:
4
x =6
34 + 4x
= 28
x
Steps to Solving Rational Equations:
1. Eliminate the fractions. Multiply both
sides by the LCD (Least Common
Denominator).
2. Eliminate any possible solutions that
would make the denominator zero.
3. You may be able to eliminate an answer
that would not make sense. (i.e. having
a negative number when the problem is
dealing with distance or time)
March 05, 2013
Rational Inequality:
* Inequalities that contain one or more
rational expressions.
Steps to Solving Rational Inequalities:
1. State the excluded values. What
makes the denominator zero.
2. Solve the related equation.
3. Use the values determined in Steps 1
and 2 to divide a number line into
regions. Test a value in each region to
determine which regions satisfy the
original inequality.
1. Solve and check.
5
2
+
24
3-x
=
1
4
March 05, 2013
2. Solve and check.
p2 - p + 1
p+1
3.
2
p -7
=
2
p -1
+p
Tim and Ashley mow lawns together. Tim working
alone could complete the job in 4.5 hours, and Ashley
could complete it alone in 3.7 hours. How long does it
take to complete the job when they are working
together?
March 05, 2013
4.
Janine swims for 5 hours in a stream that has a current
of 1 mile per hour. She leaves her dock and swims
upstream of 2 miles and then back to the dock. What
is her swimming speed in still water?
5. Solve.
2
2
1
<
+
3
3s
9s
March 05, 2013
9 - 6 Solving Rational Equations &
Inequalities
pg. 509 - 511
#2, 3, 10, 12, 14, 15, 18, 19, 22, 25, 31,
33, 37, 44 - 48, 50
19 problems