Сократите дробь (11x^2-10x-1)/(x^2-1)

Question

Сократите дробь (11x^2-10x-1)/(x^2-1)

Answer 1

(11x²-10x-1)/(x²-1)=(10x²+x²-10x-1)/(x²-1)=[10x(x-1)+(x²-1)]/(x-1)(x+1)=
=[10x(x-1)+(x-1)(x+1)]/(x-1)(x+1)=(10x+x+1)/(x+1)=(11x+1)/(x+1);