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The image you provided shows a mathematical problem written in Indonesian. The text reads:

**10. Cari himpunan penyelesaian dari pertidaksamaan \(\frac{2x + 3}{x + 1} > 2\)**

a. \( x < -\frac{5}{2}\)

b. \( x < 1\)

c. \( x > 1\)

d. \( x \in (-1, 1)\)

e. \( x \in (-1, 1) \cup (1, \infty)\)

This is an inequality problem that asks you to find the solution set of the inequality \(\frac{2x + 3}{x + 1} > 2\).

### Solving the Inequality

1. Start by subtracting 2 from both sides to simplify the inequality:
   \[
   \frac{2x + 3}{x + 1} - 2 > 0
   \]
   
2. To combine the fractions, express 2 as \(\frac{2(x + 1)}{x + 1}\):
   \[
   \frac{2x + 3 - 2(x + 1)}{x + 1} > 0
   \]
   
   Simplifying the numerator:
   \[
   \frac{2x + 3 - 2x - 2}{x + 1} > 0
   \]
   \[
   \frac{1}{x + 1} > 0
   \]

3. The inequality \(\frac{1}{x + 1} > 0\) is positive when \(x + 1 > 0\), meaning:
   \[
   x > -1
   \]

4. We must also consider the original condition to ensure that the denominator does not equal zero. So, \(x \neq -1\).

Thus, the solution set is \(x > -1\).

### Matching with the Given Options
Looking at the options, the correct answer is **e. \( x \in (-1, 1) \cup (1, \infty)\)** because this is the interval where the inequality holds true, excluding \(x = 1\) where the inequality would equal zero.

Would you like further details or have any questions?

### Related Questions:
1. How do you solve inequalities involving rational expressions?
2. What are the steps to analyze inequalities on number lines?
3. How can you determine if a rational function has discontinuities?
4. Why is it important to exclude certain values from the solution of an inequality?
5. How do inequalities differ from equations when it comes to solutions?

### Tip:
Always check the critical points where the denominator equals zero in rational inequalities, as these points often indicate boundaries or exclusions in the solution set.

Explore how to solve the inequality (2x + 3)/(x + 1) > 2 step-by-step. Understand the concept of rational expressions and fractional inequalities in mathematics. Suitable for students in Grades 10-12.

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