1. **State the problem:** Simplify the expression $$\frac{-\frac{1}{3}-\left(-3\right)}{1+\left(-\frac{1}{3}\right)\left(-3\right)}$$. 2. **Recall the formula:** This expression resembles the formula for the tangent of a difference of angles: $$\tan(a-b) = \frac{\tan a - \tan b}{1 + \tan a \tan b}$$, but here we just simplify the fraction. 3. **Simplify the numerator:** $$-\frac{1}{3} - (-3) = -\frac{1}{3} + 3 = -\frac{1}{3} + \frac{9}{3} = \frac{-1 + 9}{3} = \frac{8}{3}$$ 4. **Simplify the denominator:** $$1 + \left(-\frac{1}{3}\right) \times (-3) = 1 + \frac{3}{3} = 1 + 1 = 2$$ 5. **Rewrite the fraction:** $$\frac{\frac{8}{3}}{2}$$ 6. **Divide numerator by denominator:** $$\frac{8}{3} \div 2 = \frac{8}{3} \times \frac{1}{2} = \frac{8 \times 1}{3 \times 2} = \frac{8}{6}$$ 7. **Simplify the fraction:** $$\frac{8}{6} = \frac{\cancel{8}^{4}}{\cancel{6}^{3}} = \frac{4}{3}$$ **Final answer:** $$\frac{4}{3}$$