Ответ:
[tex]\frac{1}{10}[/tex]
Объяснение:
[tex]\frac{m^2+16n^2}{m^2-16n^2}-\frac{m+4n}{2m-8n}=\frac{m^2+16n^2}{(m-4n)(m+4n)}-\frac{m+4n}{2(m-4n)}=\\\\\frac{2(m^2+16n^2)}{2(m-4n)(m+4n)}-\frac{(m+4n)^2}{2(m-4n)(m+4n)}}=\frac{2(m^2+16n^2)-(m+4n)^2}{2(m-4n)(m+4n)}}=\\\\\frac{2m^2+32n^2-(m^2+8mn+16n^2)}{2(m-4n)(m+4n)}=\frac{2m^2+32n^2-m^2-8mn-16n^2)}{2(m-4n)(m+4n)}=\\\\\frac{m^2-8mn+16n^2}{2(m-4n)(m+4n)}=\frac{(m-4n)^2}{2(m-4n)(m+4n)}=\frac{m-4n}{2(m+4n)}[/tex]
[tex]\frac{3-4\cdot 0,5}{2\cdot (3+4\cdot 0,5)}=\frac{3-2}{2\cdot (3+2)}=\frac{1}{2\cdot 5}=\frac{1}{10}[/tex]
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Answers & Comments
Ответ:
[tex]\frac{1}{10}[/tex]
Объяснение:
[tex]\frac{m^2+16n^2}{m^2-16n^2}-\frac{m+4n}{2m-8n}=\frac{m^2+16n^2}{(m-4n)(m+4n)}-\frac{m+4n}{2(m-4n)}=\\\\\frac{2(m^2+16n^2)}{2(m-4n)(m+4n)}-\frac{(m+4n)^2}{2(m-4n)(m+4n)}}=\frac{2(m^2+16n^2)-(m+4n)^2}{2(m-4n)(m+4n)}}=\\\\\frac{2m^2+32n^2-(m^2+8mn+16n^2)}{2(m-4n)(m+4n)}=\frac{2m^2+32n^2-m^2-8mn-16n^2)}{2(m-4n)(m+4n)}=\\\\\frac{m^2-8mn+16n^2}{2(m-4n)(m+4n)}=\frac{(m-4n)^2}{2(m-4n)(m+4n)}=\frac{m-4n}{2(m+4n)}[/tex]
[tex]\frac{3-4\cdot 0,5}{2\cdot (3+4\cdot 0,5)}=\frac{3-2}{2\cdot (3+2)}=\frac{1}{2\cdot 5}=\frac{1}{10}[/tex]