B) 2x²+3x/3-x = x-x²/x-3; Г) x²-2x/2x-1 = 4x-3/1-2x; B) 5x-2/x+2 = 6x-21/x-3; Г) 2y-5/y+5 = 3y+21/2y-1; B) 3y² + y-24/9-y² = -2; Д) 4x+2/1+2x = x-6. Г) 9/x+3 = 2x-1;

Решим представленные уравнения:

1. B) $$\frac{2x^2+3x}{3-x} = \frac{x-x^2}{x-3};$$

   ОДЗ: $$x
   e 3$$

   $$\frac{2x^2+3x}{3-x} = -\frac{x-x^2}{3-x};$$

   $$2x^2+3x = -x+x^2;$$

   $$x^2+4x = 0;$$

   $$x(x+4) = 0;$$

   $$x_1 = 0;$$

   $$x_2 = -4.$$

   Ответ: $$x_1 = 0; x_2 = -4.$$

2. Г) $$\frac{x^2-2x}{2x-1} = \frac{4x-3}{1-2x};$$

   ОДЗ: $$x
   e \frac{1}{2}$$

   $$\frac{x^2-2x}{2x-1} = -\frac{4x-3}{2x-1};$$

   $$x^2-2x = -4x+3;$$

   $$x^2+2x-3 = 0;$$

   По теореме Виета:

   $$x_1+x_2 = -2;$$

   $$x_1 \cdot x_2 = -3;$$

   $$x_1 = -3;$$

   $$x_2 = 1.$$

   Ответ: $$x_1 = -3; x_2 = 1.$$

3. B) $$\frac{5x-2}{x+2} = \frac{6x-21}{x-3};$$

   ОДЗ: $$x
   e -2; x
   e 3$$

   $$(5x-2)(x-3) = (6x-21)(x+2);$$

   $$5x^2-15x-2x+6 = 6x^2+12x-21x-42;$$

   $$x^2-16x-48 = 0;$$

   $$D = 256 + 192 = 448;$$

   $$x_1 = \frac{16 + \sqrt{448}}{2} = \frac{16 + 8\sqrt{7}}{2} = 8+4\sqrt{7};$$

   $$x_2 = \frac{16 - \sqrt{448}}{2} = \frac{16 - 8\sqrt{7}}{2} = 8-4\sqrt{7}.$$

   Ответ: $$x_1 = 8+4\sqrt{7}; x_2 = 8-4\sqrt{7}.$$

4. Г) $$\frac{2y-5}{y+5} = \frac{3y+21}{2y-1};$$

   ОДЗ: $$y
   e -5; y
   e \frac{1}{2}$$

   $$(2y-5)(2y-1) = (3y+21)(y+5);$$

   $$4y^2-2y-10y+5 = 3y^2 + 15y + 21y + 105;$$

   $$y^2 - 48y - 100 = 0;$$

   $$D = 2304 + 400 = 2704;$$

   $$y_1 = \frac{48 + \sqrt{2704}}{2} = \frac{48 + 52}{2} = 50;$$

   $$y_2 = \frac{48 - \sqrt{2704}}{2} = \frac{48 - 52}{2} = -2.$$

   Ответ: $$y_1 = 50; y_2 = -2.$$

5. B) $$\frac{3y^2 + y-24}{9-y^2} = -2;$$

   ОДЗ: $$y
   e \pm 3$$

   $$3y^2 + y - 24 = -18 + 2y^2;$$

   $$y^2 + y - 6 = 0;$$

   По теореме Виета:

   $$y_1 + y_2 = -1;$$

   $$y_1 \cdot y_2 = -6;$$

   $$y_1 = -3;$$

   $$y_2 = 2.$$

   Но, $$y
   e -3$$, значит:

   Ответ: $$y = 2.$$

6. Д) $$\frac{4x+2}{1+2x} = x-6;$$

   ОДЗ: $$x
   e -\frac{1}{2}$$

   $$\frac{2(2x+1)}{2x+1} = x-6;$$

   $$x-6 = 2;$$

   $$x = 8.$$

   Ответ: $$x = 8.$$

7. Г) $$\frac{9}{x+3} = 2x-1;$$

   ОДЗ: $$x
   e -3$$

   $$9 = (2x-1)(x+3);$$

   $$9 = 2x^2+6x-x-3;$$

   $$2x^2+5x-12 = 0;$$

   $$D = 25+96 = 121;$$

   $$x_1 = \frac{-5 + \sqrt{121}}{4} = \frac{-5 + 11}{4} = \frac{3}{2};$$

   $$x_2 = \frac{-5 - \sqrt{121}}{4} = \frac{-5 - 11}{4} = -4.$$

   Ответ: $$x_1 = \frac{3}{2}; x_2 = -4.$$