Упростите пж X^2+1/x-1 : x^4-1/x-1

Question

Упростите пж X^2+1/x-1 : x^4-1/x-1

Answer 1

(x²+1)/(x-1) : (x²-1)(x²+1)/(x-1) =(x²+1)/(x-1) *(x-1)/(x-1)(x+1)(x²+1) =(x²+1) /(x-1)*(x+1)(x²+1) =1/(x-1)(x+1) =1/(x²-1)