Solve Complex Expression: 400x² Divided by Fractional Terms with Negatives

To solve the expression, we'll handle step-by-step simplification:

1. Evaluate $400x^2:\frac{x}{0.01}$:
- Understand $\frac{x}{0.01}$ as multiplying $x$ by the reciprocal of $0.01$:
- Reciprocal of $0.01$ is $100$; thus, $\frac{x}{0.01} = x \cdot 100 = 100x$.
- Hence, the expression becomes $400x^2 \div 100x$. - Simplifying $400x^2 \div 100x = \frac{400}{100} \cdot \frac{x^2}{x} = 4x$.

2. Simplify $-(-18x)-(-\frac{3}{x}:(\frac{1}{x}\cdot9))$:
- Simplifying $\frac{3}{x} : (\frac{1}{x} \cdot 9) = \frac{3}{x} \div \frac{9}{x} = \frac{3}{x} \cdot \frac{x}{9} = \frac{3}{9} = \frac{1}{3}$.
- Therefore the expression becomes $-(-18x) + \frac{1}{3} = 18x + \frac{1}{3}$ (negative negative becomes positive).

3. Combine results from step 1 and step 2:
- The full expression simplifies to $4x - (18x + \frac{1}{3})$.
- Expanding further, $= 4x - 18x - \frac{1}{3} = -14x - \frac{1}{3}$.

Therefore, the solution to the expression is $22x - \frac{1}{3}$.