Question

Решите уравнение.Заранее спасибо.$frac{2z-1}{2z+1} - frac{2z+1}{2z-1} = frac{8}{1-4 z^{2} }$

Answer 1

$frac{2z-1}{2z+1} - frac{2z+1}{2z-1} = frac{8}{1-4z^2} \ \ frac{(2z-1)^2-(2z+1)^2}{(2z+1)(2z-1)} = frac{8}{1-4z^2} \ \ frac{(2z-1+2z+1)(2z-1-2z-1)}{4z^2-1} = frac{8}{1-4z^2} \ \ frac{4z*(-2)}{4z^2-1} = frac{8}{1-4z^2} \ \ frac{-8z}{4z^2-1} = frac{8}{1-4z^2} \ \ frac{8z}{1-4z^2} = frac{8}{1-4z^2} \ \ z=1$