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Let's address both questions from the image you uploaded:

### **Pregunta 18:**
We are asked to find the least common multiple (LCM) of the following fractions:

\[
\frac{1}{x} \quad \frac{1}{x+1} \quad \frac{1}{x^2+x}
\]

1. To find the LCM of these fractions, we first need to find the LCM of their denominators.
   
   Denominators: \( x \), \( x + 1 \), and \( x^2 + x \).

   - \( x^2 + x \) can be factored as \( x(x + 1) \).

2. Now, the LCM is the product of the highest powers of each unique factor.

   Factors: \( x \) and \( x + 1 \).

   Therefore, the LCM is:
   \[
   x(x + 1)
   \]

Thus, the correct answer is: \( \boxed{x(x + 1)} \).

### **Pregunta 19:**
We are asked to solve the following operation:

\[
\frac{7}{8} + \frac{5}{12} - \frac{11}{36}
\]

1. The denominators are 8, 12, and 36. We need to find the least common denominator (LCD).
   
   - The LCD of 8, 12, and 36 is 72.

2. Rewrite each fraction with the LCD as the denominator:
   \[
   \frac{7}{8} = \frac{63}{72}, \quad \frac{5}{12} = \frac{30}{72}, \quad \frac{11}{36} = \frac{22}{72}
   \]

3. Perform the addition and subtraction:
   \[
   \frac{63}{72} + \frac{30}{72} - \frac{22}{72} = \frac{63 + 30 - 22}{72} = \frac{71}{72}
   \]

Thus, the correct answer is: \( \boxed{\frac{71}{72}} \).

---

Would you like further details or have any other questions?

### Related Questions:
1. How do you find the least common multiple of algebraic expressions?
2. What is the process for simplifying algebraic fractions?
3. How can you determine the least common denominator for three or more fractions?
4. Why is factoring useful when finding the LCM of polynomials?
5. What are some methods to add and subtract fractions with different denominators?

### Tip:
When finding the least common denominator, always factor each denominator to identify the highest powers of each factor involved!

Pregunta 18: ¿Cuál es el mínimo común múltiplo de las fracciones 1/x, 1/(x+1), y 1/(x^2 + x)?
Pregunta 19: Resuelve la operación 7/8 + 5/12 - 11/36.

Learn how to find the least common multiple (LCM) of algebraic expressions and solve fraction addition and subtraction with denominators 8, 12, and 36. Detailed step-by-step solution for Grades 9-11 students.

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