Question

спростіть вираз будьласка ​

Answer 1

Ответ:

$\dfrac{8}{p}$

Пошаговое объяснение:

$\bigg (\dfrac{m-4p}{m^{2}+4mp}-\dfrac{m+4p}{m^{2}-4mp} \bigg ) \cdot \dfrac{16p^{2}-m^{2}}{2p^{2}}=\bigg (\dfrac{m-4p}{m(m+4p)}-\dfrac{m+4p}{m(m-4p)} \bigg ) \cdot \dfrac{16p^{2}-m^{2}}{2p^{2}}=$

$=\dfrac{(m-4p)(m-4p)-(m+4p)(m+4p)}{m(m+4p)(m-4p)} \cdot \dfrac{16p^{2}-m^{2}}{2p^{2}}=\dfrac{(m-4p)^{2}-(m+4p)^{2}}{m(m^{2}-(4p)^{2})} \cdot$

$\cdot \dfrac{16p^{2}-m^{2}}{2p^{2}}=\dfrac{m^{2}-8mp+16p^{2}-(m^{2}+8mp+16p^{2})}{m(m^{2}-16p^{2})} \cdot \dfrac{16p^{2}-m^{2}}{2p^{2}}=$

$=\dfrac{m^{2}-m^{2}-8mp-8mp+16p^{2}-16p^{2}}{m(m^{2}-16p^{2})} \cdot \dfrac{16p^{2}-m^{2}}{2p^{2}}=\dfrac{-16mp}{m(m^{2}-16p^{2})} \cdot \dfrac{16p^{2}-m^{2}}{2p^{2}}=$

$=\dfrac{16p}{16p^{2}-m^{2}} \cdot \dfrac{16p^{2}-m^{2}}{2p^{2}}=\dfrac{16p}{2p^{2}}=\dfrac{8 \cdot 2 \cdot p}{2 \cdot p \cdot p}=\dfrac{8}{p};$

Answer 2

Пошаговое объяснение:

1.

Упростим выражение в скобках:

$\frac{m-4p}{m^2+4pm} -\frac{m+4p}{m^2-4pm}=\frac{m-4p}{m*(m+4p)}-\frac{m+4p}{m*(m-4p)}=\frac{(m-4p)^2-(m+4p)^2}{m*(m-4p)*(m+4p)} =\\\frac{m^2-8mp+16p^2-m^2-8mp-16p^2}{m*(m^2-16p^2)} = \frac{-16mp}{m*(-(16p^2-m^2))}= \frac{16p}{16p^2-m^2}.$

2.

$\frac{16p}{16p^2-m^2}*\frac{16p^2-m^2}{2p^2}=\frac{8}{p}.$