[tex] \frac{x + 3}{3 - x} = \frac{x}{x - 1} [/tex]
[tex](x + 3)(x - 1) = x(3 - x)[/tex]
[tex] {x}^{2} - x + 3x - 3 = 3x - {x}^{2} [/tex]
[tex] {x}^{2} + {x}^{2} - x - 3 = 0[/tex]
[tex] {2x}^{2} - x - 3 = 0[/tex]
[tex]a = 2 \\ b = - 1 \\ c = - 3[/tex]
[tex]∆ = {b}^{2} - 4ac = {( - 1})^{2} - 4 \times 2 \times ( - 3) = 1 + 24 = 25[/tex]
[tex] \sqrt{∆} = 5[/tex]
[tex] x_{1} = \frac{ - b - \sqrt{∆}}{2a} = \frac{1 - 5}{2 \times 2} = \frac{ - 4}{4} = - 1[/tex]
[tex] x_{2} = \frac{ - b + \sqrt{∆} }{2a} = \frac{1 + 5}{2 \times 2} = \frac{6}{4} = \frac{3}{2} = 1 \frac{1}{2} [/tex]
