Certainly! Let's simplify the given expression [tex]\(\frac{16x^2y^2 - 4xy}{3xy}\)[/tex] step by step.
### Step 1: Break up the Fraction
We can start by breaking up the fraction into two separate fractions:
[tex]\[
\frac{16x^2y^2 - 4xy}{3xy} = \frac{16x^2y^2}{3xy} - \frac{4xy}{3xy}
\][/tex]
### Step 2: Simplify Each Fraction Separately
#### First Fraction: [tex]\(\frac{16x^2y^2}{3xy}\)[/tex]
- Simplify the numerator and the denominator by canceling common factors:
- [tex]\[
\frac{16x^2y^2}{3xy} = \frac{16 \cdot x \cdot x \cdot y \cdot y}{3 \cdot x \cdot y}
\][/tex]
- Cancel out [tex]\(x\)[/tex] and [tex]\(y\)[/tex] from the numerator and denominator:
- [tex]\[
\frac{16x^2y^2}{3xy} = \frac{16 \cdot x \cdot y}{3}
\][/tex]
- Which simplifies to:
- [tex]\[
\frac{16xy}{3}
\][/tex]
#### Second Fraction: [tex]\(\frac{4xy}{3xy}\)[/tex]
- Simplify this fraction directly by canceling common factors:
- [tex]\[
\frac{4xy}{3xy} = \frac{4}{3}
\][/tex]
### Step 3: Combine the Simplified Fractions
Now, combine the results of the simplified fractions:
[tex]\[
\frac{16x^2y^2 - 4xy}{3xy} = \frac{16xy}{3} - \frac{4}{3}
\][/tex]
Therefore, the simplified expression is:
[tex]\[
\boxed{\frac{16xy}{3} - \frac{4}{3}}
\][/tex]
