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!