Simplify :
`7x + 4{x^(2) div(5x div 10)} - 3{2 - x^(3) div (3x^(2) div x)}`

Answer

To simplify the expression \(7x + 4\left(\frac{x^2}{\frac{5x}{10}}\right) - 3\left(2 - \frac{x^3}{\frac{3x^2}{x}}\right)\), we will follow the steps below:

### Step 1: Simplify the division inside the brackets
First, we simplify the expression inside the brackets.

1. **For the first part**:
\[ \frac{5x}{10} = \frac{1}{2}x \]
So,
\[ \frac{x^2}{\frac{5x}{10}} = \frac{x^2}{\frac{1}{2}x} = x^2 \cdot \frac{2}{x} = 2x \]

2. **For the second part**:
\[ \frac{3x^2}{x} = 3x \]
Hence,
\[ \frac{x^3}{\frac{3x^2}{x}} = \frac{x^3}{3x} = \frac{x^2}{3} \]

### Step 2: Substitute back into the expression
Now we can rewrite the original expression with the simplified parts:
\[ 7x + 4(2x) - 3\left(2 - \frac{x^2}{3}\right) \]

### Step 3: Distribute the constants
Now distribute the constants:
1. \(4(2x) = 8x\)
2. Distributing \(-3\):
\[ -3(2) + 3\left(\frac{x^2}{3}\right) = -6 + x^2 \]

### Step 4: Combine all parts
Now combine all the parts together:
\[ 7x + 8x - 6 + x^2 \]

### Step 5: Combine like terms
Combine the like terms:
\[ (7x + 8x) + x^2 - 6 = 15x + x^2 - 6 \]

### Final Answer
Thus, the simplified expression is:
\[ x^2 + 15x - 6 \]