This is a graded discussion: 100 points possible due Apr 8 DQ - Week 11 52 52 No
ID: 3138016 • Letter: T
Question
This is a graded discussion: 100 points possible due Apr 8 DQ - Week 11 52 52 Note: see "Discussion Questions Tips" (a PDF file) under "Announcements" at the left for information and guidance on discussions, or if you are stuck on what to write. Be sure to write a post of your own, and also respond to another student's post with constructive feedback, in order to receive full credit Question: What is the Least Common Denominator of rational expressions? What is the most surefire method for finding the Least Common Denominator of rational expressions? Challenge: We know that we can multiply the denominators of two rational expressions to find a common denominator. Under what circumstances will this give us the Least Common Denominator? Initial post due Sunday, 11:59 PM, EST. Discussion board closes Tuesday, 11:59 PM, ESTExplanation / Answer
The best method to find the least common denominator of rational expressions is to first find the factors of each of such denominators into the product of its lowest terms, and express any repeating
factors as powers. For example,if we have to find the least common denominator of x/8x3y2and 3y/4x2y3, then 8x3y2 will be written as 23x3y2 and 4x2y3 will be written as 22x2y3.
Next, we list the various different factors for each denominator and if a factor is common for
all of the denominators, we list only such factors to the highest powers which appear in the denominators. In the above example, the common factors that appear in the denominators are 22,x2 and y2. Thus, the least common denominator here is 22*x2*y2 = 4x2y2.
We can multiply the denominators of two rational expressions to find a common denominator, but this may not be the least common denominator of the two rational expressions as the common factors in the two denominators will also get multiplied. In the above example, the product of the two denominators is (8x3y2)*( 4x2y3) = 32x5y5, which is not the least common denominator.
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