Solve the inequality below. Give the solution using interval notation. Give all values as integers or reduced fractions. (Do not convert fractions to decimals.) \( \frac{\mathrm{x}+2}{\mathrm{x}-1} \leq 0 \)

To solve the inequality \( \frac{x+2}{x-1} \leq 0 \), we first identify where the fraction is equal to zero or undefined. The fraction is zero when the numerator \( x + 2 = 0 \) which gives \( x = -2 \). It is undefined when the denominator \( x - 1 = 0 \) which gives \( x = 1 \). Next, we analyze the intervals defined by these critical points: \( (-\infty, -2) \), \( (-2, 1) \), and \( (1, \infty) \). 1. For the interval \( (-\infty, -2) \): Choose \( x = -3 \). The inequality becomes \( \frac{-1}{-4} > 0 \) (not included). 2. For the interval \( (-2, 1) \): Choose \( x = 0 \). The inequality becomes \( \frac{2}{-1} < 0 \) (included). 3. For the interval \( (1, \infty) \): Choose \( x = 2 \). The inequality becomes \( \frac{4}{1} > 0 \) (not included). Finally, including the critical point \( -2 \) (where the fraction equals zero) but excluding \( 1 \) (where it's undefined), the solution in interval notation is: \[ (-2, 1) \]