Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations...
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Transcript of Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations...
![Page 1: Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations (aka:fractions) and breaking a rational expression into.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649eb65503460f94bbf139/html5/thumbnails/1.jpg)
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.
![Page 2: Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations (aka:fractions) and breaking a rational expression into.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649eb65503460f94bbf139/html5/thumbnails/2.jpg)
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)
![Page 3: Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations (aka:fractions) and breaking a rational expression into.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649eb65503460f94bbf139/html5/thumbnails/3.jpg)
Rational Equations and Partial Rational Equations and Partial FractionsFractions
Now with a rational Now with a rational equationequation
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![Page 4: Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations (aka:fractions) and breaking a rational expression into.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649eb65503460f94bbf139/html5/thumbnails/4.jpg)
Rational Equations and Partial Rational Equations and Partial FractionsFractions
Decompose Decompose FractionsFractions
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![Page 5: Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations (aka:fractions) and breaking a rational expression into.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649eb65503460f94bbf139/html5/thumbnails/5.jpg)
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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![Page 6: Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations (aka:fractions) and breaking a rational expression into.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649eb65503460f94bbf139/html5/thumbnails/6.jpg)
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.