1. **State the problem:** We need to find the value(s) of $x$ for which the expression $$\frac{5x+3}{6x(x+1)}$$ is undefined. 2. **Recall the rule:** A rational expression is undefined when its denominator is zero because division by zero is undefined. 3. **Set the denominator equal to zero:** $$6x(x+1) = 0$$ 4. **Solve for $x$:** Since the product is zero, either factor can be zero: - $6x = 0 \implies x = 0$ - $x + 1 = 0 \implies x = -1$ 5. **Conclusion:** The expression is undefined at $x = 0$ and $x = -1$ because these values make the denominator zero. **Final answer:** The expression is undefined for $x = 0$ and $x = -1$.