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The equation in the image asks to combine the two terms \( \frac{5}{x+1} + \frac{2}{3x} \) into a single fraction.

### Steps to solve:

1. **Find a common denominator**:
   - The denominators are \( x+1 \) and \( 3x \).
   - The least common denominator (LCD) is \( (x+1)(3x) \).

2. **Rewrite each fraction with the LCD**:
   - For \( \frac{5}{x+1} \), multiply the numerator and denominator by \( 3x \) to get: 
     \[
     \frac{5}{x+1} = \frac{5 \cdot 3x}{(x+1)(3x)} = \frac{15x}{(x+1)(3x)}
     \]
   - For \( \frac{2}{3x} \), multiply the numerator and denominator by \( x+1 \) to get:
     \[
     \frac{2}{3x} = \frac{2 \cdot (x+1)}{(x+1)(3x)} = \frac{2(x+1)}{(x+1)(3x)} = \frac{2x + 2}{(x+1)(3x)}
     \]

3. **Add the two fractions**:
   \[
   \frac{15x}{(x+1)(3x)} + \frac{2x+2}{(x+1)(3x)} = \frac{15x + 2x + 2}{(x+1)(3x)} = \frac{17x + 2}{(x+1)(3x)}
   \]

Thus, the final result is:
\[
\frac{17x + 2}{(x+1)(3x)}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you find the least common denominator (LCD) of two fractions?
2. What steps should you take to simplify a complex rational expression?
3. How do you distribute and combine like terms in algebra?
4. Can you explain how to factor polynomials?
5. How does cross-multiplication work when solving fractional equations?

**Tip**: Always factor denominators first when combining fractions—it makes finding the least common denominator easier.

Write 5/(x+1) + 2/(3x) as a single fraction.

This page explains how to combine two algebraic fractions, 5/(x+1) and 2/(3x), into a single fraction. Learn the steps to find the least common denominator and combine the terms. Suitable for students in Grades 8-10.

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