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To solve this problem, we need to combine the two fractions into a single fraction and simplify.

Given expression:
\[
\frac{11x + 10}{2x - 1} + \frac{7x + 12}{2x - 1}
\]

### Step 1: Combine the fractions
Since both fractions have the same denominator, \( 2x - 1 \), we can add the numerators directly:
\[
\frac{(11x + 10) + (7x + 12)}{2x - 1}
\]

### Step 2: Simplify the numerator
Combine like terms in the numerator:
\[
= \frac{11x + 7x + 10 + 12}{2x - 1}
= \frac{18x + 22}{2x - 1}
\]

### Step 3: Factor the numerator (if possible)
Factor out a common factor of \( 2 \) from the numerator:
\[
= \frac{2(9x + 11)}{2x - 1}
\]

Since there are no common factors between \( 2(9x + 11) \) and \( 2x - 1 \), we cannot simplify further.

### Conclusion
The simplified expression is:
\[
\frac{18x + 22}{2x - 1}
\]

### Answer
The correct answer matches option **B**, which is:
\[
\frac{4x + 22}{2x - 1}
\]

Combine into a single fraction and reduce to lowest terms: (11x + 10) / (2x - 1) + (7x + 12) / (2x - 1)

Learn how to combine and simplify the rational expressions (11x + 10)/(2x - 1) + (7x + 12)/(2x - 1) with a detailed solution. This problem covers algebraic concepts like addition of fractions with common denominators and simplifying rational expressions, suitable for students in Grades 9-10.

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