Question

Решите 5 задание (Докажите тождество)

Answer 1

$\dfrac{2x^2+4}{x^2-1}-\dfrac{x-2}{x+1}-\dfrac{x+1}{x-1}=\dfrac{2x^2+4}{(x-1)(x+1)}-\dfrac{x-2}{x+1}-\dfrac{x+1}{x-1}=\\ \\ \\ =\dfrac{2x^2+4-(x-2)(x-1)-(x+1)^2}{(x-1)(x+1)}=\dfrac{2x^2+4-x^2+3x-2-x^2-2x-1}{(x-1)(x+1)}\\ \\ \\ =\dfrac{x+1}{(x-1)(x+1)}=\dfrac{1}{x-1}$