https://file.aiquickdraw.com/mathbot/file/172959521819165j7rz1y.jpg

The given expression from the image is:

\[
\frac{2}{3x^2y} - \frac{4}{9xy^2}
\]

To simplify this expression, we need to find a common denominator.

### Step 1: Determine the Least Common Denominator (LCD)
The denominators are \( 3x^2y \) and \( 9xy^2 \). 

- Factorize the denominators:
  - \( 3x^2y \) = \( 3x^2y \)
  - \( 9xy^2 \) = \( 9xy^2 \)

The least common denominator is \( 9x^2y^2 \) because it is the least common multiple of the two denominators.

### Step 2: Rewrite both fractions with the LCD
Now we rewrite both fractions with the denominator \( 9x^2y^2 \):

\[
\frac{2}{3x^2y} = \frac{2 \cdot 3y}{3x^2y \cdot 3y} = \frac{6y}{9x^2y^2}
\]

\[
\frac{4}{9xy^2} = \frac{4 \cdot x}{9xy^2 \cdot x} = \frac{4x}{9x^2y^2}
\]

### Step 3: Subtract the fractions
Now that the fractions have the same denominator, we can subtract the numerators:

\[
\frac{6y}{9x^2y^2} - \frac{4x}{9x^2y^2} = \frac{6y - 4x}{9x^2y^2}
\]

So, the simplified expression is:

\[
\frac{6y - 4x}{9x^2y^2}
\]

Would you like to go into more detail on any part of this solution? 

Here are 5 related questions to explore:
1. How do you find the least common denominator for more complex fractions?
2. What happens if one denominator is a constant instead of a variable expression?
3. How can you simplify expressions involving multiple variables and powers?
4. How would you approach simplifying if the numerators also had variables?
5. Can this expression be factored further for certain values of \(x\) and \(y\)?

**Tip:** When simplifying fractions with variables, always check for common factors that can cancel across the numerator and denominator.

Simplify the expression: 2/(3x^2y) - 4/(9xy^2)

Learn how to simplify the rational expression 2/(3x^2y) - 4/(9xy^2) by finding the least common denominator and subtracting the fractions. This step-by-step solution explains the core algebraic concepts and is suitable for students in Grades 8-10.

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