#4 ### Finding the Lowest Common Denominator (LCD)In this exercise, we aim to find the lowest common denominator for the given fractions. The fractions are as follows:\[\frac{3a^2}{a^2 + a + 1}, \quad \frac{2a}{a - 1}, \quad \frac{a^3}{a^3 - 1}\]The options for the lowest common denominator are:- \((a^3 - 1)(a^2 + a + 1)\)- \((a + 1)^2(a - 1)\)- \(a^3 - 1\)To find the LCD, we must first factorize the denominators (if possible) and then determine the least common multiple.1. For the fraction \(\frac{3a^2}{a^2 + a + 1}\), the denominator \(a^2 + a + 1\) cannot be further factored using real numbers.2. For the fraction \(\frac{2a}{a - 1}\), the denominator \(a - 1\) is already in its simplest form.3. For the fraction \(\frac{a^3}{a^3 - 1}\), we can factorize \(a^3 - 1\) as follows: \[ a^3 - 1 = (a - 1)(a^2 + a + 1) \]Given these factors, the least common multiple of the denominators must include each distinct factor the maximum number of times it appears in any factorization. Here, the common denominator is the product of \((a - 1)\) and \((a^2 + a + 1)\):Hence, the lowest common denominator is:\[(a^3 - 1)(a^2 + a + 1)\]Thus, the correct option is:- \((a^3 - 1)(a^2 + a + 1)\)This concludes the analysis for finding the lowest common denominator for the given fractions.

Name: #4 ### Finding the Lowest Common Denominator (LCD)In this exercise, we
Uploaded: 2024-03-05T11:52:21.000Z
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Description: #4 ### Finding the Lowest Common Denominator (LCD)In this exercise, we aim to find the lowest common denominator for the given fractions. The fractions are as follows:\[\frac{3a^2}{a^2 + a + 1}, \quad \frac{2a}{a - 1}, \quad \frac{a^3}{a^3 - 1}\]The