Question

encontre a soluçao da equaçao fracionaria x+1 sob x-2=x-3

Answer 1

$\frac{x+1}{x-2} = x-3\\(x-2)(x-3) = x+1\\x^2 - 3x - 2x + 6 = x + 1\\x^2 - 5x - x + 6 - 1 = 0\\x^2 - 6x + 5 = 0\\\Delta = (-6)^2 - 4 \cdot 1 \cdot 5\\\Delta = 36 - 20\\\Delta = 16\\\\x = \frac{-(-6)\pm \sqrt{16}}{2 \cdot 1} = \frac{6\pm4}{2} = 3 \pm 2\\\\x_1 = 3 + 2 = 5\\x_2 = 3 - 2 = 1\\\\\\\boxed{\boxed{S = \{ 1, \ 5\}}}$