6b)++Simplifying,+multiplying,+dividing+rationals

Multiplying, dividing and simplifying fractions is relatively easy, as long as you follow the simple rules we have known for years. Simplifying, multiplying, and dividing rational expressions is not much different. In this section, it is important to remember a few important skills. This is how to factor rational expressions, FOIL, cancel when variables are put to certain powers, and multiplying and dividing fractions. Before reviewing this section, it may be a good idea to look back at these skills, and refresh your memory so that simplifying, multiplying, and dividing rationals will be an easy task.

It is important to know that before you begin to divide or multiply rationals, that each part of the numerator and denominator are fully simplified. This may be done by cancelling, or factoring. If you don't simplify, you could run into many more errors on your way to your final answer. Factoring quadratics and cubics is an important skill as Mr. Killian has reminded us. YOU MUST KNOW HOW TO DO THIS FOR THIS SECTION! We know that when multiplying fractions, you can just multiply across with no problem. However, when dividing, you must flip the denominator and numerator of the divisor and then multiply across. If you refresh your mind on these simple skills, the following section will be a piece of cake to review.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut9_mulrat.htm

http://www.purplemath.com/modules/rtnlmult2.htm

TUTORIAL - EXAMPLE 1- SIMPLIFYING RATIONALS __(y 2 +25)__ (y 2 -5y) __(y+5)(y-5)__ y(y-5)

__y+5__ y

EXAMPLE 2- MULTIPLICATION OF RATIONALS __y-4__ x __5__ (y-1) (y-4)

__(y-4)5__ (y-1)(y-4)

__5__ (y-1)

__5__ y-1 EXAMPLE 3- DIVISION OF RATIONALS

__(y-10) (y+10)__ / __(y-10)__ (y-9) ) -1

__(y-10) (y+10)__ x -__1__ (y -9) (y-10)

__(y-10)(y+10)(-1)__ (y-9)(y-10)

__(y+10)(-1)__ (y-9)

__-1y -10__ y-9