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The given expression is:

\[
\frac{3(2b + 3)}{4} + \frac{b}{10}
\]

Let's simplify the expression step by step:

### Step 1: Expand the first term
Expand the numerator of the first fraction:

\[
3(2b + 3) = 6b + 9
\]

So, the expression becomes:

\[
\frac{6b + 9}{4} + \frac{b}{10}
\]

### Step 2: Find a common denominator
The common denominator for 4 and 10 is 20. Let's rewrite both terms with 20 as the denominator.

For the first fraction:

\[
\frac{6b + 9}{4} = \frac{5(6b + 9)}{20} = \frac{30b + 45}{20}
\]

For the second fraction:

\[
\frac{b}{10} = \frac{2b}{20}
\]

### Step 3: Combine the fractions
Now that both fractions have the same denominator, we can combine them:

\[
\frac{30b + 45}{20} + \frac{2b}{20} = \frac{30b + 45 + 2b}{20} = \frac{32b + 45}{20}
\]

Thus, the simplified expression is:

\[
\frac{32b + 45}{20}
\]

Let me know if you'd like more details or explanations!

Here are some related questions for practice:
1. How would you simplify \(\frac{4(3x + 5)}{2} + \frac{x}{5}\)?
2. What would the result be if you factored the numerator \(32b + 45\)?
3. How would you solve this expression for \(b\) if it were set equal to a value?
4. Can you identify an example of when finding a common denominator is useful in real life?
5. What changes if one of the terms in the expression is a negative value?

**Tip**: When simplifying algebraic fractions, finding a common denominator is key to combining terms easily!

Simplify the expression: (3(2b + 3) / 4) + (b / 10)

Learn how to simplify the algebraic expression (3(2b + 3) / 4) + (b / 10) step-by-step. This problem covers core algebraic concepts like expanding expressions, finding a common denominator, and combining fractions. Suitable for students in Grades 8-10.

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