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Combining like terms is a fundamental concept in algebra that helps in simplifying expressions. Like terms are terms that have the same variables raised to the same power. For this exercise, we notice the fractions \( \frac{2}{5} \) and \( -\frac{2}{5} \). These are like terms because they both have the denominator 5. When terms are alike, we can add or subtract them to simplify the expression. For instance, combining \( \frac{2}{5} \) and \( -\frac{2}{5} \) results in 0 (i.e., \( \frac{2}{5} - \frac{2}{5} = 0 \)). This is because the same values with opposite signs cancel each other out. By recognizing and combining like terms, you clean up the expression and make it easier to manage.

Adding fractions can often cause confusion, but it's straightforward once you understand the steps. The key is to find a common denominator. In this exercise, however, since we are adding and subtracting fractions where the like terms cancel each other out, we only have the fraction \( \frac{5}{12} \) left. When adding fractions with the same denominator, you simply add the numerators. However, if the denominators were different, you would need to find the least common denominator (LCD) first. Once the denominators are the same, you can add the numerators and keep the common denominator unchanged. Adding \( \frac{2}{5} \), \( \frac{5}{12} \), and \( -\frac{2}{5} \) simplifies to just \( \frac{5}{12} \) because the \( \frac{2}{5} \) and \( -\frac{2}{5} \) cancel each other out.

Simplifying expressions involves making them as concise and readable as possible. This often means performing operations to combine like terms and simplify fractions. In this exercise, after combining like terms, the expression \( \frac{2}{5} + \frac{5}{12} + \frac{-2}{5} \) becomes \[ \frac{5}{12} + 0. \] Adding 0 to any number does not change its value, so the final simplified expression is just \( \frac{5}{12} \). Simplification helps in making the expression easier to understand and work with. Steps to simplify typically include:

• Combining like terms
• Adding and subtracting fractions
• Reducing fractions to their simplest forms

Following these steps ensures that your expressions are as straightforward as possible.