Вопрос от посетителя
Очень интересное выражение!
Упростите:
Отвечает Илюха:
=[/tex]
=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” title=”=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” alt=”=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” />
=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” title=”=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” alt=”=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” />
=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=” title=”frac{sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}}}{sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}}}=” title=”=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=” title=”frac{sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}}}{sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}}}=” alt=”=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=” title=”frac{sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}}}{sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}}}=” />
=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” title=”=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” alt=”=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” />
=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” title=”=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” alt=”=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” />
=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=” alt=”frac{sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}}}{sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}}}=” title=”=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=” alt=”frac{sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}}}{sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}}}=” alt=”=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=” alt=”frac{sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}}}{sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}}}=” />
=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” title=”=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” alt=”=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}==” />
=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” title=”=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” alt=”=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}=” />
[tex]=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=” />
^2+2(m^2-4)+(m-2)^2}{m^2-4}}{frac{(m+2)^2-(m-2)^2}{m^2-4}}= "=frac{frac{(m+2)^2+2(m^2-4)+(m-2)^2}{m^2-4}}{frac{(m+2)^2-(m-2)^2}{m^2-4}}=")
(m^2-4)}{(m^2+4m+4-m^2+4m-4)(m^2-4)}= "=frac{(m^2+4m+4+2m^2-8+m^2-4m+4)(m^2-4)}{(m^2+4m+4-m^2+4m-4)(m^2-4)}=")
