(х+3)/(х+2)+(х+2)/(х+3)=(х+5)/(х+4)+(х+8)/(х+7)

   1. Выделим целую часть дробей:

• (х + 3)/(х + 2) + (х + 2)/(х + 3) = (х + 5)/(х + 4) + (х + 8)/(х + 7);
• 1 + 1/(х + 2) + 1 - 1/(х + 3) = 1 + 1/(х + 4) + 1 + 1/(х + 7);
• 1/(х + 2) - 1/(х + 3) = 1/(х + 4) + 1/(х + 7).

   2. Умножим обе части на (х + 2)(х + 3)(х + 4)(х + 7):

• 1/((х + 2)(х + 3)) = (2x + 11)/((х + 4)(х + 7));
• (х + 4)(х + 7) = (2x + 11)(х + 2)(х + 3);
• x^2 + 11x + 28 = (2x + 11)(х^2 + 5x + 6);
• x^2 + 11x + 28 = 2x^3 + 21x^2 + 67x + 66;
• 2x^3 + 20x^2 + 56x + 38 = 0;
• x^3 + 10x^2 + 28x + 19 = 0;
• x^3 + x^2 + 9x^2 + 9x + 19x + 19 = 0;
• x^2(x + 1) + 9x(x + 1) + 19(x + 1) = 0;
• (x + 1)(x^2 + 9x + 19) = 0;

   1) x + 1 = 0;

      x = -1;

   2) x^2 + 9x + 19 = 0;

• D = 9^2 - 4 * 19 = 81 - 76 = 5;
• x = (-9 5)/2.

   Ответ: -1; (-9 5)/2.