Question

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Упростите:

 

Answer 1

$frac{sqrt{frac{m 2}{m-2}} sqrt{frac{m-2}{m 2}}}{sqrt{frac{m 2}{m-2}}-sqrt{frac{m-2}{m 2}}}</var>=$</p> <p> </p> <p><img src=[/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}})}==" />

 

$<var>=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}</var>=$

 

$<var>=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=$

 

$<var>=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}=</var>=$

 

$<var>=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}</var>=$

 

$frac{sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}}}{sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}}}</var>=$

 

$<var>=frac{(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}}-sqrt{frac{m-2}{m+2}})(sqrt{frac{m+2}{m-2}}+sqrt{frac{m-2}{m+2}})}=</var>=$

 

$<var>=frac{(sqrt{frac{m+2}{m-2}})^2+2sqrt{frac{m+2}{m-2}}sqrt{frac{m-2}{m+2}}+(sqrt{frac{m-2}{m+2}})^2}{(sqrt{frac{m+2}{m-2}})^2-(sqrt{frac{m-2}{m+2}})^2}</var>=$

 

$<var>=frac{frac{m+2}{m-2}+2sqrt{frac{m+2}{m-2}cdot frac{m-2}{m+2}}+frac{m-2}{m+2}}{frac{m+2}{m-2}-frac{m-2}{m+2}}=" /></var></p> <p> </p> <p>[tex]=frac{frac{(m+2)^2+2(m^2-4)+(m-2)^2}{m^2-4}}{frac{(m+2)^2-(m-2)^2}{m^2-4}}=$

 

$=frac{(m^2+4m+4+2m^2-8+m^2-4m+4)(m^2-4)}{(m^2+4m+4-m^2+4m-4)(m^2-4)}=$

 

$=frac{4m^2}{8m}=frac{m}{2}$