Question

Найдите значение выражения.

Answer 1

$\dfrac{a}{b}=0,5\\\\\\\dfrac{(3a+b)^{-2}-(3a-b)^{-2}}{(3a-b)^{-2}+(3a+b)^{-2}}=\dfrac{\frac{1}{(3a+b)^2}-\frac{1}{(3a-b)^2}}{\frac{1}{(3a-b)^2}+\frac{1}{(3a+b)^2}}=\dfrac{(3a-b)^2-(3a+b)^2}{(3a+b)^2+(3a-b)^2}=\\\\\\=\dfrac{9a^2-6ab+b^2-(9a^2+6ab+b^2)}{9a^2+6ab+b^2+(9a^2-6ab+b^2)}=\dfrac{-12ab}{18a^2+2b^2}=-\dfrac{6ab}{9a^2+b^2}=\Big[\; \dfrac{:ab}{:ab}\; \Big]=$

$=-\dfrac{6}{9\cdot \frac{a}{b}+\frac{b}{a}}=-\dfrac{6}{9\cdot 0,5+\frac{1}{0,5}}=-\dfrac{6}{4,5+2}=-\dfrac{6}{6,5}=-\dfrac{60}{65}=-\dfrac{12}{13}$