Question

Find the least common den (3x)/(x-6) and (9)/(x+2)

Answer 1

The least common denominator (LCD) for
`\((3x)/(x-6)\) and \(\frac{9}`
`{x+2}\)` is
`\((x-6)(x+2)\)`.

Step-by-step explanation:

To find the LCD, we need to identify the unique factors in the denominators of both fractions and ensure that each factor appears in the LCD the greatest number of times it appears in any one denominator.

The denominators are
`\(x-6\)` and
`\(x+2\)`. The LCD must include both factors and should account for the maximum number of times each factor appears in either denominator.

Therefore, the LCD is
`\((x-6)(x+2)\)`. This ensures that each denominator is covered, as
`\((x-6)\) and \((x+2)\)` are both present and accounted for, considering their respective appearances in the original denominators.

In summary, the least common denominator for
`\((3x)/(x-6)\) and \((9)/(x+2)\) is \((x-6)(x+2)\).`