решите уравнение: 4/(x-2)+3/(x-4)=2/(x-6)+1/(x-8)

 4/(x - 2) + 3/(x - 4) = 2/(x - 6) + 1/(x - 8);

4 * (x – 4) * (x – 6) * (x – 8) + 3 * (x - 2) * (x – 6) * (x – 8)  = 2 * (x - 2) * (x – 4) * (x – 8) + 1 * (x - 2) * (x – 4) * (x – 6); 

Перенесем все значения выражения на одну сторону и получим: 

4 * (x – 4) * (x – 6) * (x – 8) + 3 * (x - 2) * (x – 6) * (x – 8)  -  2 * (x - 2) * (x – 4) * (x – 8) – 1 * (x - 2) * (x – 4) * (x – 6) = 0; 

Сгруппируем подобные и вынесем за скобки общий множитель и получим: 

(x – 4) * (x – 8) * (4 * (x – 6) – 2 * (x – 2)) + (x – 2) * (x – 6) * (3 * (x – 8) – 1 * (x – 4)) = 0;

(x – 4) * (x – 8) * (4 * x - 24 – 2 * x + 4) + (x – 2) * (x – 6) * (3 * x – 24 – x  + 4) = 0;

(x – 4) * (x – 8) * (2 * x - 20) + (x – 2) * (x – 6) * (2 * x - 20) = 0;

(2 * x – 20) * ((x – 4) * (x – 8) + (x – 2) * (x – 6)) = 0; 

(2 * x - 20) * (x ^ 2 - 8 * x - 4 * x + 32 + x ^ 2 - 6 * x - 2 * x + 12) = 0; 

(2 * x - 20) * (2 * x ^ 2 - 20 * x + 44) = 0; 

(x - 10) * (x ^ 2 - 10 * x + 22) = 0; 

{ x - 10 = 0; 

x ^ 2 - 10 * x + 22 = 0; 

{ x = 10; 

x = 5 + √3; 

x = 5 - √3.