CHAPTER 8 REVIEW

PROCEDURES FOR RATIONAL EXPRESSIONS (Fractions)

SIMPLE FRACTIONS

Reducing simple fractions- one polynomial in the numerator and one in the denominator
*Factor the numerator ( top of the fraction)
*Factor the denominator (bottom of the fraction)
*Reduce common terms in the numerator and denominator (using the identity property)

MULTIPLYING/DIVIDING FRACTIONS

Multiplying fractions, you multiply across the top and across the bottom and reduce common terms as in simple fractions above
Dividing fractions you multiply the numerator by the reciprocal of the denominator
(Flip the bottom fraction and use the flipped term to multiply the top fraction)

ADDITION AND SUBTRACTION OF FRACTIONS

*Find the LCD- Least Common Denominator from all the fractions being added/subtracted
*Make each fraction have the same denominator by using the identity property to multiply the top and bottom of each
            fraction by the missing part of the LCD
*Combine and simplify the numerators of all the fractions
*Place the combined and simplified numerator over the denominator
*Simplify if possible using the procedures from simple fractions provided above (factor the
           numerator and denominator and reduce like terms)
NOTE: The denominator does not go away!!!!!!

COMPLEX FRACTIONS

Method #1
*Create a fraction in the numerator using the addition rules provided above
*Create a fraction in the denominator using the addition rules provided above
*Invert the denominator and use this fraction to multiply the numerator as described above
*Reduce common terms using the identity property as you did in simple fractions above

Method #2
*Find the LCD of all the fractions in the top and bottom of the complex fraction
*Multiple every fraction in the top and bottom by the LCD and reduce each fraction
*Simplify and reduce the denominator and numerator if possible

SOLVING EQUATIONS WHICH CONTAIN FRACTIONS

*Find the LCD of all the fractions in the equation, both right side and left side of the equal sign
*Multiply each and every term on both sides of the equal sign by the LCD
*Reduce the fractions (The denominators do go away)
*Solve the remaining equation
*Check your answer by substituting the result back into the original equation
*Take special care to make sure no denominator in any fraction becomes zero. If any
           denominator does become zero then the result is not acceptable and the answer becomes no solution or null set.