6c)++Adding+and+Subtracting+rational+expressions

In this lesson we will be exploring the steps needed to add or subtract rational expressions. In order to do this we will be using common denominators to add and subtract **only** the numerators of these expressions. Therefore prior knowledge to these two parts of fractions will help you to know the basics before we start our lesson: understanding what an LCD (least common denominator) is, and factoring monomials, binomials, and trinomials. Once the LCD is found, each fraction must be multiplied by whatever will give it the LCD previously found. Because the rational expressions now have the same denominator, you can simply add fractions any way that a normal fraction would be added together. You add the content in the numerators together, and the answer will have the same LCD as the starting fractions. Once you add, and you get one fraction, you can factor/simplify if necessary.

Examples:

Example 1: .

Step 1: Find the LCD of both denominators to begin (refer to lesson 5d to review factoring of trinomials)
 * [[image:http://wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut10ex5b.gif width="88" height="48"]] The first denominator is a trinomial which can be factored down to these two factors.

The second denominator is also a trinomial and can be factored the same way into two factors. ||

We are left with this as the LCD after making sure to include every factored piece and the highest exponent

Step 2: Using the LCD to rewrite fractions into equivalent fractions

Rewriting the first expression by using the new LCD

Since the denominator is missing the factor (x-8), like the common denominator we just made has, we then multiply this factor to the bottom and top of the expression

Since the denominator is missing the factor (x+5), like the common denominator we just made has, we then multiply this factor to the bottom and top of the expression; just as we did with the other expression

Step 3: Combining newly created expressions using like terms

Subtract both expressions in the numerators by combining like terms as if they were not over a denominator. (make sure to distribute negative when subtracting) Next wrtie new expression of common denominator.

Step 4: Reducing to lowest terms

Finally, factor the numerator completely making sure that there are no factors left to divide out of the expression. Keep in mind that the factors from the denominator cannot be the domain due to the fact that they make the original denominator equal to zero.



http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut10_addrat.htm__**
 * __LINKS

http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Adding-and-Subtracting-Rational-Expressions.topicArticleId-38949,articleId-38904.html