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**Solving Rational Equations**

Section 6.6 Solving Rational Equations

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**Definition A rational equation is an equation that contains**

one or more rational expressions. Examples: Goal: Clear Fractions

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**Solving Rational Equations**

1) Factor each denominator completely to find LCD 2) Multiply both sides by the LCD to clear the fractions 3) Solve the resulting equation 4) Check all possible solutions in the original equation

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**Example Solve the equation 1 Multiply both sides by the LCD 7 3 1**

LCD is 21x 21x 21x 21x 1 1 1 Solve the resulting equation

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**Example Solve 1 Multiply both sides by the LCD 1 1 1 LCD is 5b 5b 5b**

Solve the resulting equation Check the solution in the original equation

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**Example Solve the equation Multiply both sides by the LCD 1 1 (q+5)**

LCD is (q+5) (q+5) (q+5) 1 1 Solve the resulting equation No Solution

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More Examples Solve the following equations

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**Solving for a specified variable**

Isolate the specified variable in a formula The answer is another formula (not a numerical value)

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**Example Solve for R Multiply both sides by the LCD 1 LCD is (R+r)**

NO! Subtracting rI on both sides Dividing both sides by I

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**Example Solve for b 1 Multiply both sides by the LCD 1 1 1 abf LCD is**

Solve the resulting equation Move the term containing b to the left Factor out common factor b Divide both sides by f – a

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More Examples Solve the following equations

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