1. 3.4 Solving Rational Equations and Radical Equations
Solve rational equations.
Solve radical equations.
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Rational Equations
Equations containing rational expressions are called rational equations.
Solving such equations requires multiplying both
sides by the least common denominator (LCD) to
clear the equation of fractions.
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Example
Solve:
Solution: Multiply both sides by the LCD 6.
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Example (continued)
The possible solution is 5.
Check:
TRUE
The solution is 5.
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Example
Solve:
Solution: Multiply both sides by the LCD x  3.
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Example (continued)
The possible solutions are –3 and 3.
Check x = –3:
Check x = 3:
TRUE
Not Defined
The number 3 checks, so it is a solution.
Division by 0 is not defined, so 3 is not a solution.
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Radical Equations
A radical equation is an equation in which variables appear in one or more radicands. For example:
The Principle of Powers
For any positive integer n:
If a = b is true, then an = bn is true.
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8. Solving Radical Equations
To solve a radical equation we must first isolate the radical on one side of the equation.
Then apply the Principle of Powers.
When a radical equation has two radical terms on one side, we isolate one of them and then use the principle of powers. If, after doing so, a radical terms remains, we repeat these steps.
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Example
Solve
Solution
Check x = 5:
TRUE
The solution is 5.
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Example
Solve:
Solution: First, isolate the radical on one side.
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Example (continued)
The possible solutions are 9 and 2.
Check x = 9.
Check x = 2.
TRUE
FALSE
Since 9 checks but 2 does not, the only solution is 9.
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