1. **State the problem:** Simplify the expression $\frac{(3x+1)(x-4)}{3x^2 - 11x - 4}$. 2. **Write down the expression:** $$\frac{(3x+1)(x-4)}{3x^2 - 11x - 4}$$ 3. **Factor the denominator:** We need to factor $3x^2 - 11x - 4$. 4. **Find two numbers that multiply to $3 \times (-4) = -12$ and add to $-11$:** These numbers are $-12$ and $1$. 5. **Rewrite the middle term:** $$3x^2 - 12x + x - 4$$ 6. **Group terms:** $$(3x^2 - 12x) + (x - 4)$$ 7. **Factor each group:** $$3x(x - 4) + 1(x - 4)$$ 8. **Factor out common binomial:** $$(3x + 1)(x - 4)$$ 9. **Rewrite the original expression with factored denominator:** $$\frac{(3x+1)(x-4)}{(3x+1)(x-4)}$$ 10. **Cancel common factors:** $$\frac{\cancel{(3x+1)}\cancel{(x-4)}}{\cancel{(3x+1)}\cancel{(x-4)}} = 1$$ **Final answer:** $$1$$