![(\frac{m^2}{m+5}-\frac{m^3}{m^2+10m+25}):(\frac{m}{m+5}-\frac{m^2}{m^2-25})=\frac{5m-m^2}{m+5} (\frac{m^2}{m+5}-\frac{m^3}{m^2+10m+25}):(\frac{m}{m+5}-\frac{m^2}{m^2-25})=\frac{5m-m^2}{m+5}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bm%5E2%7D%7Bm%2B5%7D-%5Cfrac%7Bm%5E3%7D%7Bm%5E2%2B10m%2B25%7D%29%3A%28%5Cfrac%7Bm%7D%7Bm%2B5%7D-%5Cfrac%7Bm%5E2%7D%7Bm%5E2-25%7D%29%3D%5Cfrac%7B5m-m%5E2%7D%7Bm%2B5%7D)
![(\frac{m^2(m+5)}{(m+5)(m+5)}-\frac{m^3}{(m+5)^2}):(\frac{m(m-5)}{(m+5)(m-5)}-\frac{m^2}{(m-5)(m+5)})=\frac{5m-m^2}{m+5} (\frac{m^2(m+5)}{(m+5)(m+5)}-\frac{m^3}{(m+5)^2}):(\frac{m(m-5)}{(m+5)(m-5)}-\frac{m^2}{(m-5)(m+5)})=\frac{5m-m^2}{m+5}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bm%5E2%28m%2B5%29%7D%7B%28m%2B5%29%28m%2B5%29%7D-%5Cfrac%7Bm%5E3%7D%7B%28m%2B5%29%5E2%7D%29%3A%28%5Cfrac%7Bm%28m-5%29%7D%7B%28m%2B5%29%28m-5%29%7D-%5Cfrac%7Bm%5E2%7D%7B%28m-5%29%28m%2B5%29%7D%29%3D%5Cfrac%7B5m-m%5E2%7D%7Bm%2B5%7D)
![\frac{m^3+5m^2-m^3}{(m+5)(m+5)}:\frac{m^2-5m-m^2}{(m+5)(m-5)}=\frac{5m-m^2}{m+5} \frac{m^3+5m^2-m^3}{(m+5)(m+5)}:\frac{m^2-5m-m^2}{(m+5)(m-5)}=\frac{5m-m^2}{m+5}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%5E3%2B5m%5E2-m%5E3%7D%7B%28m%2B5%29%28m%2B5%29%7D%3A%5Cfrac%7Bm%5E2-5m-m%5E2%7D%7B%28m%2B5%29%28m-5%29%7D%3D%5Cfrac%7B5m-m%5E2%7D%7Bm%2B5%7D)
![\frac{5m^2}{(m+5)(m+5)}*\frac{(m+5)(m-5)}{-5m}=\frac{5m-m^2}{m+5} \frac{5m^2}{(m+5)(m+5)}*\frac{(m+5)(m-5)}{-5m}=\frac{5m-m^2}{m+5}](https://tex.z-dn.net/?f=%5Cfrac%7B5m%5E2%7D%7B%28m%2B5%29%28m%2B5%29%7D%2A%5Cfrac%7B%28m%2B5%29%28m-5%29%7D%7B-5m%7D%3D%5Cfrac%7B5m-m%5E2%7D%7Bm%2B5%7D)
![\frac{-m(m-5)}{m+5}=\frac{5m-m^2}{m+5} \frac{-m(m-5)}{m+5}=\frac{5m-m^2}{m+5}](https://tex.z-dn.net/?f=%5Cfrac%7B-m%28m-5%29%7D%7Bm%2B5%7D%3D%5Cfrac%7B5m-m%5E2%7D%7Bm%2B5%7D)
![\frac{5m-m^2}{m+5}=\frac{5m-m^2}{m+5} \frac{5m-m^2}{m+5}=\frac{5m-m^2}{m+5}](https://tex.z-dn.net/?f=%5Cfrac%7B5m-m%5E2%7D%7Bm%2B5%7D%3D%5Cfrac%7B5m-m%5E2%7D%7Bm%2B5%7D)
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x≠0;
Методом подбора конечно быстрее, но будем решать для школы, по обычному:
y=x² замена
y+64/y=65; умножим на y;
y²+64=65y;
y²-65y+64=0; решим квадратное уравнение
D=65²-4*64=63²
y=(65-63)/2=1;
y=(65+63)/2=64;
x²=1; x=-1;x=1;
x²=64; x=-8;x=8;
чему равно x-8/x?
8-1=7; -8+1=-7;
1-1=0; -1+1=0;
три ответа: 0; -7; 7;