Question

Знайдіть область визначення функції
Найдите область определения функции

Answer 1

$y=\dfrac{\dfrac{1}{x-1}-\dfrac{1}{x+1}}{\dfrac{1}{x-1}+\dfrac{1}{x+1}}\\\\\\OOF:\ \ \ \left\{\begin{array}{l}x-1\ne 0\ ,\\x+1\ne 0\ ,\\\dfrac{1}{x-1}+\dfrac{1}{x+1}\ne 0\ ,\end{array}\right\ \ \left\{\begin{array}{l}x\ne 1\ ,\\x\ne -1\ ,\\\dfrac{x+1+x-1}{(x-1)(x+1)}\ne 0\ ,\end{array}\right\ \ \left\{\begin{array}{l}x\ne 1\ ,\\x\ne -1\ ,\\\dfrac{2x}{(x-1)(x+1)}\ne 0\ ,\end{array}\right\ \$

$\left\{\begin{array}{l}x\ne 1\ ,\\x\ne -1\ ,\\x\ne 0\ ,\end{array}\right\ \ \ \ \Rightarrow \ \ \ \ x\in (-\infty;-1\ )\cup (-1\, ;\ 0\ )\cup (\ 0\ ;1\ )\cup (\ 1\ ;+\infty \, )$