It seems like you're working with an algebraic expression. I believe the expression you've provided is:

\[
\frac{21abc}{18b^2c}
\]

Let's simplify this expression step by step:

1. **Cancel out common factors**:  
   Both the numerator and denominator have common terms that we can cancel out. Specifically, \( b \) and \( c \) appear in both the numerator and denominator.

   - In the numerator: \( 21abc \)
   - In the denominator: \( 18b^2c \)

2. **Simplifying the coefficients**:
   \[
   \frac{21}{18} = \frac{7}{6}
   \]

3. **Simplifying the variables**:
   - \( a \) remains in the numerator.
   - \( b \): In the numerator we have \( b^1 \), and in the denominator, we have \( b^2 \). So \( b \) simplifies to \( \frac{1}{b} \).
   - \( c \): Since \( c \) appears in both the numerator and denominator, they cancel each other out.

Thus, the simplified expression is:

\[
\frac{7a}{6b}
\]

### Final Answer:
\[
\frac{7a}{6b}
\]

Would you like further details or have any questions?

Here are some related questions:
1. What happens if \( b = 0 \) in this expression?
2. Can this expression be simplified further if \( a \), \( b \), or \( c \) have specific values?
3. How would this expression change if we had an exponent on \( a \)?
4. What if we replaced \( c \) with another variable, like \( d \)?
5. How would this expression look if both \( a \) and \( b \) had negative exponents?

**Tip**: When simplifying algebraic fractions, always look for common factors in both the numerator and denominator to make the process easier!

Learn how to simplify the algebraic expression 21abc/18b^2c with a detailed step-by-step solution. This problem involves canceling common factors and simplifying variables, covering key algebraic concepts suitable for students in Grades 7-9.

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