Let's solve the equation:

\[
\frac{\left(\frac{x}{3} + \frac{2x}{5}\right)}{x+2} \div 3 = \frac{11}{15}
\]

### Step 1: Simplify the expression inside the left-hand side
Start by combining the terms inside the parentheses:

\[
\frac{x}{3} + \frac{2x}{5}
\]

To add these fractions, find a common denominator. The least common denominator of 3 and 5 is 15, so:

\[
\frac{x}{3} = \frac{5x}{15}, \quad \frac{2x}{5} = \frac{6x}{15}
\]

Now, combine them:

\[
\frac{x}{3} + \frac{2x}{5} = \frac{5x}{15} + \frac{6x}{15} = \frac{11x}{15}
\]

### Step 2: Substitute back into the equation
Now, substitute this back into the original equation:

\[
\frac{\left(\frac{11x}{15}\right)}{x+2} \div 3 = \frac{11}{15}
\]

Dividing by 3 is the same as multiplying by \(\frac{1}{3}\):

\[
\frac{\frac{11x}{15}}{x+2} \times \frac{1}{3} = \frac{11}{15}
\]

Simplifying the left-hand side:

\[
\frac{11x}{15} \times \frac{1}{3} = \frac{11x}{45}
\]

Now the equation becomes:

\[
\frac{\frac{11x}{45}}{x+2} = \frac{11}{15}
\]

### Step 3: Cross-multiply
Now, cross-multiply to solve for \(x\):

\[
11x \times 15 = 11 \times 45 (x+2)
\]

Simplifying both sides:

\[
165x = 495(x + 2)
\]

### Step 4: Expand and solve for \(x\)
Expand the right-hand side:

\[
165x = 495x + 990
\]

Now, subtract \(495x\) from both sides:

\[
165x - 495x = 990
\]

Simplify:

\[
-330x = 990
\]

Divide by \(-330\):

\[
x = \frac{990}{-330} = -3
\]

### Final Answer:
The solution to the equation is \(x = -3\).

Would you like further clarification or details on any of the steps?

Here are 5 related questions for practice:
1. Solve \(\frac{\left(\frac{2x}{3} + \frac{3x}{4}\right)}{x+1} \div 2 = \frac{5}{12}\).
2. Simplify \(\frac{\left(\frac{x}{2} + \frac{3x}{5}\right)}{x+3}\).
3. Solve \(\frac{2x + 3}{5} = \frac{4x + 7}{3}\).
4. What is the value of \(x\) in \(\frac{3x + 1}{x+4} = \frac{7}{5}\)?
5. Solve \(2x + 3 = \frac{5x + 8}{4}\).

**Tip:** Always find the least common denominator when adding or subtracting fractions to simplify the process.

Learn how to solve the fractional equation (((x/3)+(2x/5))/(x+2))/3 = 11/15 step by step. This problem involves simplifying complex fractions, cross-multiplication, and solving for x. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation