9-6 SOLVING
RATIONAL EQUATIONS
& INEQUALITIES
Objectives:
1) The student will be able to solve rational equations.
2) The student will be able to solve rational inequalities.
Rational Equations…
• Include any equation that contains one or more rational expressions.
• Example:
• Are easier to solve of the fractions are eliminated.
• This can be accomplished by multiplying each side of the equation by the
least common denominator (LCD)
• Remember: when multiplying each side by the LCD, EACH TERM ON
EACH SIDE must be multiplied.
Example 1: Solve the rational equation. Then check your solution.
Example 2: Solve the rational equation. Then check your solution.
Example 3: Solve the rational equation. Then check your solution.
Example 4: Solve the rational equation. Then check your solution.
r2 - 5 r2 + r + 2
r+ 2
=
r -1
r +1
Application
(see text p. 507)
When building the Chunnel, the English and French each started drilling on opposite
sides of the English Channel. The two sections became one in 1990. The French used
more advanced drilling machinery than the English. Suppose the English could drill the
Chunnel in 6.2 years and the French could drill it in 5.8 years. How long would it have
taken the two countries to drill the tunnel?
Rational Inequalities…
• Contain one or more rational expressions.
Steps to Solve:
1) State the excluded values.
2) Solve the related equation.
3) Use these values to divide a number line into regions.
Test a value in each region to determine which regions
satisfy the original inequality.
Example 5: Solve the rational inequality.
1
5 1
+ >
4x 8x 2
Example 6: Solve the rational inequality.
4
>1
c+2
Example 7: Solve the rational inequality.
1 1 1
+
<
3y 4y 2
Homework
Text p. 509 # 3
Text p. 510 #s 12-26 even