Find the least common denominator​ (LCD) of StartFraction 6 x Over x plus 1 EndFraction
 
and StartFraction 6 Over 7 x plus 7 EndFraction
.

To find the least common denominator (LCD) of two rational expressions, we need to find the least common multiple (LCM) of their denominators.

Given the two expressions:

1. \( \frac{6x}{x + 1} \)
2. \( \frac{6}{7x + 7} \)

### Step 1: Factor the denominators.
- Denominator of the first expression: \( x + 1 \) (This is already in its simplest form).
- Denominator of the second expression: \( 7x + 7 \). We can factor out a 7:
  \[
  7x + 7 = 7(x + 1)
  \]

### Step 2: Find the least common denominator (LCD).
Now that we have the denominators \( x + 1 \) and \( 7(x + 1) \), the least common denominator will be the least common multiple of these two denominators. Since the second denominator contains \( 7(x + 1) \), the LCD is:

\[
\text{LCD} = 7(x + 1)
\]

Thus, the least common denominator of the two expressions is \( 7(x + 1) \).

Would you like to explore how to rewrite the fractions with this common denominator or have more details on any step?

Here are 5 related questions:
1. How do you simplify rational expressions?
2. What is the method to find the LCM of polynomials?
3. How do you factor polynomials involving higher degrees?
4. Can you convert complex fractions into simpler forms?
5. How do you solve rational equations involving different denominators?

**Tip:** Always factor polynomials to their simplest form before finding the least common denominator!

Find the least common denominator​ (LCD) of StartFraction 6x Over x + 1 EndFraction and StartFraction 6 Over 7x + 7 EndFraction.

Discover how to find the least common denominator (LCD) of the rational expressions 6x/(x + 1) and 6/(7x + 7). Learn step-by-step how to factor the denominators and determine the LCD, covering essential algebraic concepts. Suitable for students in Grades 8-10.

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