1. The problem asks why the least common denominator (LCD) is $6(x+1)$. 2. The LCD is the smallest expression that all denominators in a set of fractions can divide into without leaving a remainder. 3. To find the LCD, factor each denominator into prime factors and variables. For example, if denominators are $2$, $3$, and $(x+1)$, their prime factors are $2$, $3$, and $(x+1)$. 4. The LCD must include each factor the greatest number of times it appears in any denominator. Here, $2$ and $3$ combine to $6$, and $(x+1)$ is a factor from one denominator. 5. Therefore, the LCD is $6(x+1)$ because it includes all prime factors and variables needed to clear denominators in the problem. 6. This ensures all fractions can be rewritten with the same denominator, facilitating addition, subtraction, or comparison.