Rational Equations and Partial Rational Equations and Partial FractionsFractions

The purpose of this lesson is solving The purpose of this lesson is solving Rational Equations (aka:fractions) Rational Equations (aka:fractions) and breaking a rational expression and breaking a rational expression into partial fractions (called into partial fractions (called Decomposition of Fractions)Decomposition of Fractions)

The use: solving equations with The use: solving equations with fractions, developing a sense of logic fractions, developing a sense of logic on how fractions can be broken down on how fractions can be broken down in to parts.in to parts.

Rational Equations and Partial FractionsRational Equations and Partial Fractions

Solving Rational Equations can be Solving Rational Equations can be solved by converting to a common solved by converting to a common denominator or multiplying both denominator or multiplying both sides of an equation by the LCD.sides of an equation by the LCD.

Find the LCD: make a product of the Find the LCD: make a product of the different factors to the highest different factors to the highest power.power.

Example: 3(x-1)Example: 3(x-1)22(x+2), 5(x-1)(x+2), 5(x-1)(x+2)(x+2)33(x-5)(x-5)

Rational Equations and Partial Rational Equations and Partial FractionsFractions

Now with a rational Now with a rational equationequation

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Rational Equations and Partial Rational Equations and Partial FractionsFractions

Decompose Decompose FractionsFractions

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Rational Equations and Partial Rational Equations and Partial FractionsFractions

Solving Rational Solving Rational InequalitiesInequalities

Find f(x)=0 values Find f(x)=0 values from numerator and from numerator and excluded values excluded values from the from the denominatordenominator

Lay those points out Lay those points out on a number line and on a number line and test convenient test convenient points for truth or points for truth or consequencesconsequences

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Rational Equations and Partial Rational Equations and Partial FractionsFractions

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Find denominator exclusions, then multiply both sides by lcd and solve.Place values on number line and test regions for truth by using convenient values.