Calculate

Apuntes

Let's evaluate the limit: \[ \lim_{x \to -1} \frac{-x^2 + 3x - 2}{3x^2 + 2x - 5} \] **Step 1: Substitute \(x = -1\) directly to check for indeterminate form.** Numerator: \[ -(-1)^2 + 3(-1) - 2 = -1 - 3 - 2 = -6 \] Denominator: \[ 3(-1)^2 + 2(-1) - 5 = 3(1) - 2 - 5 = 3 - 2 - 5 = -4 \] Since the numerator is \(-6\) and the denominator is \(-4\), neither is zero, and the limit is simply: \[ \frac{-6}{-4} = \frac{6}{4} = \frac{3}{2} \] **Final answer:** \[ \boxed{\frac{3}{2}} \]