https://file.aiquickdraw.com/mathbot/file/1726603194978cp4ulth8.jpg

The given expression in the image is:

\[
\frac{1}{3x} + \frac{1}{5x}
\]

Let's solve this step by step.

### Step 1: Find a common denominator.
The denominators are \(3x\) and \(5x\). The least common denominator (LCD) is \(15x\), as the least common multiple of 3 and 5 is 15.

### Step 2: Rewrite each fraction with the common denominator.

\[
\frac{1}{3x} = \frac{5}{15x} \quad \text{(multiplying numerator and denominator by 5)}
\]
\[
\frac{1}{5x} = \frac{3}{15x} \quad \text{(multiplying numerator and denominator by 3)}
\]

### Step 3: Add the fractions.

\[
\frac{5}{15x} + \frac{3}{15x} = \frac{5 + 3}{15x} = \frac{8}{15x}
\]

### Final answer:

\[
\frac{8}{15x}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you find the least common denominator (LCD) for any two fractions?
2. What is the procedure for adding algebraic fractions?
3. How do you simplify complex rational expressions?
4. How does finding the LCD differ when variables are involved?
5. What are other methods to simplify expressions involving fractions?

### Tip:
When dealing with fractions that have variables in the denominator, always check if you can factor or cancel terms to simplify the expression further.

This solution walks through the process of adding two algebraic fractions: 1/(3x) + 1/(5x). Learn how to find the least common denominator (LCD) and simplify the expression to 8/(15x). Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation