1. The problem involves simplifying the expression $\frac{x+3}{5x+4}$ and solving the equation $x^{1}-1=0$. 2. For the expression $\frac{x+3}{5x+4}$, note that it is a rational expression and cannot be simplified further unless factoring is possible, which it is not here. 3. For the equation $x^{1}-1=0$, this simplifies to $x-1=0$ because $x^{1}=x$. 4. Solve $x-1=0$ by adding 1 to both sides: $x=1$. 5. Therefore, the solution to the equation is $x=1$. 6. The expression $\frac{x+3}{5x+4}$ remains as is unless a specific value of $x$ is given. Final answer: The solution to the equation is $x=1$ and the expression $\frac{x+3}{5x+4}$ is simplified as much as possible.