1. We are asked to divide the polynomial $2x^2 + x - 3$ by $x - 1$. 2. Polynomial division formula: $$\frac{\text{Dividend}}{\text{Divisor}} = \text{Quotient} + \frac{\text{Remainder}}{\text{Divisor}}$$ 3. Set up the division: divide $2x^2$ by $x$ to get $2x$. 4. Multiply $2x$ by $x - 1$ to get $2x^2 - 2x$. 5. Subtract this from the original polynomial: $$\left(2x^2 + x - 3\right) - \left(2x^2 - 2x\right) = \cancel{2x^2} + x - 3 - \cancel{2x^2} + 2x = 3x - 3$$ 6. Divide $3x$ by $x$ to get $3$. 7. Multiply $3$ by $x - 1$ to get $3x - 3$. 8. Subtract this from the remainder: $$\left(3x - 3\right) - \left(3x - 3\right) = \cancel{3x} - 3 - \cancel{3x} + 3 = 0$$ 9. Since the remainder is $0$, the division is exact. 10. The quotient is $2x + 3$. **Final answer:** $$\frac{2x^2 + x - 3}{x - 1} = 2x + 3$$