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Finding the Least Common Denominator for Rational Expressions

Learn how to determine the least common denominator (LCD) for given rational expressions with clear examples. This guide details the steps for calculating the LCD using factored forms of denominators. For instance, to find the LCD of the expressions 8/3x and 5/2, we identify the factors of each denominator and calculate the highest power of each factor. You'll also explore another example involving fractions with different denominators and see how to combine them effectively. Perfect for strengthening your understanding of rational expressions!

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Finding the Least Common Denominator for Rational Expressions

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  1. Standard 45 Determine a common denominator for a given rational expression By Karlee Nesvik and Mackenzie Brown

  2. Find the LCD of example 8/3x, 5/2 Step 1: Factor all the denominators. The first denominator "3x" has two factors, 3 and x. The second denominator "2" has only one factor, 2.

  3. Cont. Step 2: The LCD is the list of all the DIFFERENT factors in the denominators raised to the highest power that there is of each factor. Putting all the different factors together, we get (3)(x)(2) = 6x for our LCD. So, 6x would be the LCD of the two rational expression of 8/3x, 5/2

  4. Another Example: 3X/4 + X/8 3X x 2/ 4 x 2 + X/8 = 6X/8+ X/8= 7X/8 The Least Common Denominator (LCD) is 8. Multiply BOTH the top and bottom of the first fraction by 2 to create the common denominator. Remember, when adding "like" variables, add only the numbers in front of the variables (the coefficients).

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