https://file.aiquickdraw.com/mathbot/file/1725309163911zduvk2m2.jpg

To solve Example 2 in the image, let's proceed step by step.

### Example 2:
The equation given is:
\[
\frac{3}{x} - \frac{1}{2} = 1
\]

#### Step 1: Find the Least Common Denominator (LCD)
The denominators in the equation are \(x\) and \(2\). The least common denominator (LCD) will be \(2x\).

#### Step 2: Multiply both sides by the LCD
Multiply every term in the equation by \(2x\) to eliminate the denominators:
\[
2x \times \left(\frac{3}{x}\right) - 2x \times \left(\frac{1}{2}\right) = 2x \times 1
\]

Simplifying each term:
\[
2 \cdot 3 - x = 2x
\]
\[
6 - x = 2x
\]

#### Step 3: Simplify the equation
To solve for \(x\), add \(x\) to both sides to get all the \(x\) terms on one side of the equation:
\[
6 = 3x
\]

#### Step 4: Solve for \(x\)
Divide both sides by 3:
\[
x = \frac{6}{3} = 2
\]

### Final Answer:
\[
x = 2
\]

Would you like more details or have any questions? Here are 5 related questions you might find useful:

1. How would the solution change if the equation was \(\frac{3}{x} - \frac{1}{4} = 1\)?
2. Can you solve a similar equation where the denominators are different, such as \(\frac{2}{x+1} + \frac{3}{4} = 1\)?
3. What is the significance of finding the least common denominator in equations with fractions?
4. How would you check your solution to ensure it is correct?
5. How does multiplying by the LCD help simplify the equation?

**Tip:** Always check your solution by substituting it back into the original equation to verify that both sides are equal.

Learn how to solve Example 2: an equation with fractions involving finding the least common denominator and step-by-step solving techniques. Suitable for students in Grades 7-9.

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