The problem asks to find the least common denominator (LCD) of the fractions $\frac{9}{x-7}$ and $\frac{6}{x^2 - 14x + 49}$.

1. Problem Description

The problem asks to find the least common denominator (LCD) of the fractions $\frac{9}{x-7}$ and $\frac{6}{x^2 - 14x + 49}$.

2. Solution Steps

To find the LCD, we need to factor each denominator.

The first denominator is $x-7$. This is already in its simplest form.

The second denominator is $x^2 - 14x + 49$. We can factor this as follows:

$x^2 - 14x + 49 = (x-7)(x-7) = (x-7)^2$.

The LCD is the least common multiple of the denominators. In this case, we have $x-7$ and $(x-7)^2$.

The LCD is $(x-7)^2$.

3. Final Answer

$(x-7)^2$