Question

find the least common denominator of \\(dfrac{12x}{x - 1}\\) and \\(dfrac{x}{x - 6}\\).

Explanation:

Step1: Identify denominators

The denominators are \(x - 1\) and \(x - 6\).

Step2: Determine LCD for polynomials

For two distinct linear denominators (no common factors), the least common denominator (LCD) is the product of the denominators. So multiply \((x - 1)\) and \((x - 6)\).
$$(x - 1)(x - 6)=x^2-6x - x + 6=x^2-7x + 6$$

Answer:

The least common denominator is \((x - 1)(x - 6)\) (or \(x^2 - 7x + 6\)).