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2. Rational Expressions
* Equivalent versus Equal
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3. Definitions
Equation ­ a statement of equality between two expressions.
eg.a) 2x + 3 = 5 b) 2x + 3 = 3x + 5
Open Sentence ­ an equation that may or not be true
Solution or root ­ the value of the variable that makes the equation
true.
The root or solution is said to satisfy the equation.
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4. Fractional or Rational Equation ­ an equation with a variable in a
denominator.
Eg. 2 + 1
__ __
= 10
x 2x
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5. Steps to Solving a Rational Equation
1) Factor each rational equation, if needed.
2) Find the LCD
3) Find non­permissible values
4) Multiply both sides of the equation by the LCD
5) Simplify
6) Solve the resulting equivalent equation.
7) Eliminate extraneous roots from the solution.
Extraneous roots ­ a solution to an equation that is a non­permissible
value
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6. Example 1
x
__ + 3x
3 = 2 + __
2 4
Check
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7. Example 2
__
4 + 6 = 2
x
Check
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8. Example 3
x
_____ 5
___
=
x + 2 7
Check
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9. Example 4
4 3
___ ___ 11
x + = ___
2x 4
Check
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10. Assignment
p. 179 Questions 1 ­16 odd
p. 185 Questions 1 ­ 29 odd
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