Lesson 8-6: Solving Rational
Equations and Inequalities
Let’s review some old skills

How do you find the LCM of two monomials
–
8x2y3 and 18x5
* Why do we find LCM’s with rational expressions?
Old Skills Cont…

What is it called when two fractions are equal
to each other?

What process do we use to solve a problem
like this?
To solve a rational equation:
1. Find the common denominator
2. Multiply both sides of the equation by the
LCD
3. Solve for x
4. Check your answer
Examples

Solve
1 x 1
 
2 5 9
2
3
  10
x3 2
Let’s put those old skills to new
use…
Solve
.
Solve
.
Check your solution.
2x
x 2  x  10
3


x  5 x 2  8 x  15 x  3
Examples

Solve
7n
5
3n


3n  3 4n  4 2n  2
Bill’s garden hose can fill the pool in 12 hours.
His neighbor has a hose that can fill the pool
in 15 hours. How long will it take to fill the
pool using both hoses?
Joe can complete his yard work in 3 hours. If
his son helps it will only take 2 hours working
together. How long would the yard work take
if his son was working alone?
Lesson 8-6: Day #2
Rational Inequalities
Solving Rational Inequalities
Divide a numberline into intervals using answers from
steps 1 and 2 to create intervals
Test a value in each interval to determine which values
satisfy the inequality
Examples

Solve
x
1
x 1


3 x2
4
Examples

Solve
x2
1
x4


x2 x2 x2