https://file.aiquickdraw.com/mathbot/file/17266033495186o304jha.jpg

The problem shown is:

\[
\frac{2}{x+2} + \frac{3}{x+4}
\]

To solve this, we need to add the two fractions by finding a common denominator.

### Step 1: Find the common denominator
The denominators are \(x+2\) and \(x+4\), so the least common denominator (LCD) is \((x+2)(x+4)\).

### Step 2: Rewrite the fractions with the common denominator
\[
\frac{2}{x+2} + \frac{3}{x+4} = \frac{2(x+4)}{(x+2)(x+4)} + \frac{3(x+2)}{(x+2)(x+4)}
\]

### Step 3: Simplify the numerators
Expand the numerators:

\[
2(x+4) = 2x + 8
\]
\[
3(x+2) = 3x + 6
\]

Now, the expression becomes:

\[
\frac{2x + 8}{(x+2)(x+4)} + \frac{3x + 6}{(x+2)(x+4)}
\]

### Step 4: Combine the fractions
Now that the denominators are the same, we can combine the numerators:

\[
\frac{(2x + 8) + (3x + 6)}{(x+2)(x+4)} = \frac{5x + 14}{(x+2)(x+4)}
\]

### Final Answer:
\[
\frac{5x + 14}{(x+2)(x+4)}
\]

Would you like further details on any step or additional explanations? Here are some related questions to explore:

1. How do you find the least common denominator of two rational expressions?
2. What is the process of expanding binomials like \(2(x+4)\)?
3. How do you simplify complex fractions involving polynomials?
4. What is the importance of factoring in algebraic expressions?
5. How do restrictions on variables arise in rational expressions?

**Tip:** When adding fractions with different denominators, always find the least common denominator and rewrite both fractions before combining them.

Simplify the expression 2/(x+2) + 3/(x+4).

Learn how to simplify the expression 2/(x+2) + 3/(x+4) by finding the least common denominator and combining terms. This problem covers essential algebraic concepts related to rational expressions and is suitable for students in Grades 8-10.

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