Simplify the following :
`(2""4/5-1""3/5) div (3""3/5-2""1/5)`.

Answer

To simplify the expression \( (2 \frac{4}{5} - 1 \frac{3}{5}) \div (3 \frac{3}{5} - 2 \frac{1}{5}) \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

- For \( 2 \frac{4}{5} \):
\[ 2 \frac{4}{5} = \frac{(2 \times 5) + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \]

- For \( 1 \frac{3}{5} \):
\[ 1 \frac{3}{5} = \frac{(1 \times 5) + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} \]

- For \( 3 \frac{3}{5} \):
\[ 3 \frac{3}{5} = \frac{(3 \times 5) + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5} \]

- For \( 2 \frac{1}{5} \):
\[ 2 \frac{1}{5} = \frac{(2 \times 5) + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5} \]

### Step 2: Substitute Back into the Expression
Now we can substitute these improper fractions back into the expression:
\[ \left( \frac{14}{5} - \frac{8}{5} \right) \div \left( \frac{18}{5} - \frac{11}{5} \right) \]

### Step 3: Perform the Subtraction
Now, we perform the subtraction in both the numerator and the denominator:

- In the numerator:
\[ \frac{14}{5} - \frac{8}{5} = \frac{14 - 8}{5} = \frac{6}{5} \]

- In the denominator:
\[ \frac{18}{5} - \frac{11}{5} = \frac{18 - 11}{5} = \frac{7}{5} \]

### Step 4: Rewrite the Division as Multiplication
Now we can rewrite the division of fractions:
\[ \frac{6}{5} \div \frac{7}{5} = \frac{6}{5} \times \frac{5}{7} \]

### Step 5: Simplify the Expression
Now we can simplify:
\[ \frac{6 \times 5}{5 \times 7} = \frac{6}{7} \]

### Final Answer
Thus, the simplified form of the expression is:
\[ \frac{6}{7} \]

---