Section 6'4 Equations Involving Rational Expressions

1
Section 6.4 Equations Involving Rational
Expressions

• Page 378

2
Clear Denominators

• In general when you see an equation that has a
  rational expression, multiply both sides by the
  LCD to clear all of the denominators.

3
Example 3
4
Rational Equation
Now we must check the proposed solution.
5
Check
x 2, 4
No Zeros allowed in Denominators
True
6
Rational Equation

• Since the solution leads to a zero in the
  denominator we must reject this answer.
• Hence the solution is the null set. x or x ?

7
Solving Equations with Rational Expressions

• Step 1 Multiply each side by the least common
  denominator (this clears fractions)
• Step 2 Solve the resulting equation.
• Step 3 Check each proposed solution by
  substituting it in the original equation.

8
Example 4
9
Example
First note the factoring
What is the LCD?
10
Example
11
If we multiply both sides of the equation by (x
5), we get 6 6.
Is the solution set all real numbers?
12
42
13
22
Check
Since x 5 is in the domain this answer will
check.
14
13
15
Homework 6.4 p. 382 1-51 eoo Every Other Odd