Rational Equations and Partial Fractions The purpose of this lesson is solving Rational Equations (aka:fractions) and breaking a rational expression into partial fractions (called Decomposition of Fractions) The purpose of this lesson is solving Rational Equations (aka:fractions) and breaking a rational expression into partial fractions (called Decomposition of Fractions) The use: solving equations with fractions, developing a sense of logic on how fractions can be broken down in to parts. The use: solving equations with fractions, developing a sense of logic on how fractions can be broken down in to parts.

Rational Equations and Partial Fractions Solving Rational Equations can be solved by converting to a common denominator or multiplying both sides of an equation by the LCD. Solving Rational Equations can be solved by converting to a common denominator or multiplying both sides of an equation by the LCD. Find the LCD: make a product of the different factors to the highest power. Find the LCD: make a product of the different factors to the highest power. Example: 3(x-1) 2 (x+2), 5(x-1)(x+2) 3 (x-5) Example: 3(x-1) 2 (x+2), 5(x-1)(x+2) 3 (x-5)

Rational Equations and Partial Fractions Now with a rational equation Now with a rational equation

Rational Equations and Partial Fractions Decompose Fractions Decompose Fractions

Rational Equations and Partial Fractions Solving Rational Inequalities Solving Rational Inequalities Find f(x)=0 values from numerator and excluded values from the denominator Find f(x)=0 values from numerator and excluded values from the denominator Lay those points out on a number line and test convenient points for truth or consequences Lay those points out on a number line and test convenient points for truth or consequences

Rational Equations and Partial Fractions 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.