Solve the equation \(\frac{3}{x-2} - \frac{2}{x+3} = 1\) over the interval \([-5, 4]\)

Step 1 ：Multiply through by the common denominator to clear fractions: \(3(x+3) - 2(x-2) = (x-2)(x+3)\)

Step 2 ：Simplify the equation: \(3x + 9 - 2x + 4 = x^2 + x - 6\)

Step 3 ：Rearrange to form a quadratic equation: \(x^2 - x - 13 = 0\)

Step 4 ：Apply the quadratic formula to solve for x: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{1 \pm \sqrt{53}}{2}\)

Step 5 ：Calculate the two potential solutions: \(x = \frac{1 + \sqrt{53}}{2}\) and \(x = \frac{1 - \sqrt{53}}{2}\)

Step 6 ：Check which solutions fall within the given interval \([-5, 4]\): \(x = \frac{1 + \sqrt{53}}{2}\) is approximately 3.58, which is in the interval, and \(x = \frac{1 - \sqrt{53}}{2}\) is approximately -3.58, which is also in the interval