Question

3x/(x-1)+4 /(x+1)=6/(x^2-1) ,если можно подробно

Answer 1

  1.  x≠1, x≠-1
[3x(x+1)+4(x-1)] / (x-1)(x+1)=6/(x²-1)
[3x²+7x-4] / (x²-1)= 6/(x²-1)
[3x²+7x-4-6] / (x²-1)=0
[3x²+7x-10] /(x²-1)=0
3x²+10x-3x-10=x(3x+10)-(3x+10)=(3x+10)(x-1),
(x²-1)=(x-1)(x+1) 
[(3x+10)(x-1)]  / [(x-1)(x+1)]=(3x+10) /(x+1), тогда:
 (3x+10) /(x+1)=0 
3x+10=0,  x=-10/3,  Ответ: x=-10/3