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Section 6'4 Equations Involving Rational Expressions

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Step 3 Check each proposed solution by substituting it in the original equation. Example 4 ... Check. Since x = 5 is in the domain this answer will check. #13 ... – PowerPoint PPT presentation

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Title: 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
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