[tex]1) \\ \frac{x(x - 2)}{ {x}^{2} - 4 } = 0 \\ \\ {x}^{2} - 4≠0 \\ {x}^{2} ≠ 4 \\ x≠2 \: \: \: \: \: x≠ - 2 \\ \\ \frac{x(x - 2)}{(x - 2)(x + 2)} = 0 \\ \\ \frac{x}{x + 2} = 0 \\ \\ x = 0 [/tex]
[tex]2) \\ \frac{4 - x}{x + 1} = \frac{10 - 3x}{x + 4} \\ \\ x + 1 ≠0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 4≠0\\ x≠ - 1 \: \: \: \: \: \: \: \: \: \: \: \: \: x≠ - 4 \\ \\ (4 - x)(x + 4) = (10 - 3x)(x + 1) \\ 4x + 16 - {x}^{2} - 4x = 10x + 10 - 3 {x}^{2} - 3x \\ - {x}^{2} + 16 = - 3 {x}^{2} + 7x + 10 \\ - {x}^{2} + 3 {x}^{2} - 7x + 16 - 10 =0 \\ 2 {x}^{2} - 7x + 6 = 0 \\ ∆ = ( - 7 {)}^{2} - 4 \times 2 \times 6 = 49 - 48 = 1 \\ \sqrt{∆} = \sqrt{1} = 1 \\ x_{1} = \frac{ - ( - 7) + 1}{2 \times 2} = \frac{7 + 1}{4} = \frac{8}{4} = 2 \\ x_{2} = \frac{7 - 1}{4} = \frac{6}{4} = \frac{3}{2} [/tex]
[tex]3) \frac{3x - 5}{x + 1} = 4 \\ \\ x + 1≠0 \\ x≠ - 1 \\ \\ 3x - 5 = 4(x + 1) \\ 3x - 5 = 4x + 4 \\ 3x - 4x = 4 + 5 \\ - x = 9 \\ x = - 9[/tex]
