Question

Доведи тотожність.
(m-4/m+4 - m+4/m-4) : 32m/m^2-16

Answer 1

$\displaystyle\bf\\\Big(\frac{m-4}{m+4} -\frac{m+4}{m-4} \Big):\frac{32m}{m^{2}-16 } =\\\\\\=\frac{(m-4)\cdot(m-4)-(m+4)\cdot(m+4)}{(m+4)(m-4)}:\frac{32m}{m^{2} -16} =\\\\\\=\frac{m^{2} -8m+16-(m^{2} +8m+16)}{m^{2} -16} \cdot\frac{m^{2} -16}{32m} =\\\\\\=\frac{m^{2} -8m+16-m^{2} -8m-16}{m^{2} -16} \cdot\frac{m^{2} -16}{32m} =\\\\\\=\frac{-16m}{32m} =-\frac{1}{2}=-0,5$