Find the least common denominator (LCD). $$ \frac{d}{(5 d-2)(d-7)} ; \frac{6}{(5 d-2)(d+4)} $$

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The denominators of the two fractions are:

$$
(5d-2)(d-7) \quad \text{and} \quad (5d-2)(d+4)
$$

**Step 1: Identify the factors in each denominator.**

- The first denominator has factors $$5d-2$$ and $$d-7$$.
- The second denominator has factors $$5d-2$$ and $$d+4$$.

**Step 2: Determine the least common denominator (LCD).**

To form the LCD, include each distinct factor the maximum number of times it appears in any of the denominators.

- The factor $$5d-2$$ appears in both denominators.
- The factor $$d-7$$ appears only in the first denominator.
- The factor $$d+4$$ appears only in the second denominator.

Thus, the LCD is:

$$
(5d-2)(d-7)(d+4)
$$

**Answer:**

$$
\text{LCD} = (5d-2)(d-7)(d+4)
$$
The least common denominator (LCD) is $$ (5d-2)(d-7)(d+4) $$.

Find the least common denominator (LCD). \[ \frac{d}{(5 d-2)(d-7)} ; \frac{6}{(5 d-2)(d+4)} \]

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