\( \left\{\begin{array}{l}3x^{2}-x+3 \\x^{2}-x+4\end{array}\right. \)

It looks like you've provided a system of equations or a set of expressions. However, it's not clear what you would like to do with them. If you want to solve the equations, we can set them equal to each other or analyze them further. Here are the two expressions you've provided: 1. \( 3x^2 - x + 3 \) 2. \( x^2 - x + 4 \) If you want to find the values of \( x \) for which these two expressions are equal, we can set them equal to each other: \[ 3x^2 - x + 3 = x^2 - x + 4 \] Now, let's simplify this equation: 1. Subtract \( x^2 - x + 4 \) from both sides: \[ 3x^2 - x + 3 - (x^2 - x + 4) = 0 \] 2. This simplifies to: \[ 3x^2 - x + 3 - x^2 + x - 4 = 0 \] 3. Combine like terms: \[ (3x^2 - x^2) + (-x + x) + (3 - 4) = 0 \] This results in: \[ 2x^2 - 1 = 0 \] 4. Now, solve for \( x \): \[ 2x^2 = 1 \] \[ x^2 = \frac{1}{2} \] \[ x = \pm \frac{1}{\sqrt{2}} = \pm \frac{\sqrt{2}}{2} \] Thus, the solutions to the equation \( 3x^2 - x + 3 = x^2 - x + 4 \) are: \[ x = \frac{\sqrt{2}}{2} \quad \text{and} \quad x = -\frac{\sqrt{2}}{2} \] If you have a different question or need further assistance, please let me know!