Simplify the expression. \( \frac{2 x^{2}+x-1}{x+1} \) \( \frac{2 x^{2}+x-1}{x+1}=\square \) (Simplify your answer.)

To simplify the expression \( \frac{2x^2 + x - 1}{x + 1} \), we start by factoring the numerator. The quadratic expression \( 2x^2 + x - 1 \) can be factored as \( (2x - 1)(x + 1) \). So we have: \[ \frac{2x^2 + x - 1}{x + 1} = \frac{(2x - 1)(x + 1)}{x + 1} \] Now we can cancel out \( x + 1 \) from the numerator and the denominator, provided \( x \neq -1 \): \[ = 2x - 1 \] Thus, the simplified expression is: \[ \frac{2x^2 + x - 1}{x + 1} = 2x - 1 \quad (x \neq -1) \]