(x+3/x+7) - (6/x+7) = 140/x^2-49

(x + 3)/(x + 7) - 6/(x + 7) = 140/(x^2 - 49);  

Упростим уравнение. 

(x + 3)/(x + 7) - 6/(x + 7) = 140/((x - 7) * (x + 7)); 

(x + 3)/(x + 7) * (x + 7) * (x - 7) - 6/(x + 7) * (x + 7) * (x - 7) = 140/((x - 7) * (x + 7)) * (x + 7) * (x - 7);  

(x + 3 ) * (x - 7) - 6 * (x - 7) = 140; 

Раскроем скобки. 

x^2 - 7 * x + 3 * x - 3 * 7 - 6 * x + 6 * 7 = 140; 

x^2 - 4 * x - 21 - 6 * x + 42 = 140; 

x^2 - 10 * x - 21 + 42 = 140; 

x^2 - 10 * x + 21 = 140; 

x^2 - 10 * x + 21 - 140 = 0; 

x^2 - 10 * x - 119 = 0; 

D = 100 - 4 * 1 * (-119) = 576 = 24^2; 

x1 = (10 + 24)/2 = 34/2 = 17; 

x2 = (10 - 24)/2 = -14/2 = -7; 

Ответ: х = 17 и х = -7.