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

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