Предмет: Алгебра,
автор: регина07
1/2+(3m/1-3m+2m/3m+1)*9m2-6m+1/6m2+10m
Ответы
Автор ответа:
0
1![frac{1}{2} + ( frac{3m}{1-3m } + frac{2m}{3m+1} ) * frac{9m^2-6m +1}{6m^2+10m} = \ \
= frac{1}{2} + frac{3m(3m+1) -2m (3m-1)}{-(3m-1)(3m+1)} * frac{(3m-1)^2}{2m(3m+5)} = \ \
= frac{3}{2} + frac{9m^2+3m -6m^2+2m}{-(3m-1)(3m+1)} * frac{(3m-1)^2}{2m(3m+5)} = \ \
= frac{1}{2} + frac{3m^2+5m }{- (3m-1)(3m+1)} * frac{(3m-1)^2}{2(3m^2+5m)} = \ \
= frac{3m+1}{2(3m+1)} - frac{2(3m-1)}{3m+1 } =
= frac{-3m+3}{2(3m+1)} = 1.5 * frac{1-m}{3m+1}](https://tex.z-dn.net/?f=+frac%7B1%7D%7B2%7D+%2B+%28+frac%7B3m%7D%7B1-3m+%7D+%2B++frac%7B2m%7D%7B3m%2B1%7D+%29+%2A++frac%7B9m%5E2-6m+%2B1%7D%7B6m%5E2%2B10m%7D+%3D++%5C++%5C+%0A%3D++frac%7B1%7D%7B2%7D+%2B+++frac%7B3m%283m%2B1%29+-2m+%283m-1%29%7D%7B-%283m-1%29%283m%2B1%29%7D+%2A++frac%7B%283m-1%29%5E2%7D%7B2m%283m%2B5%29%7D++%3D++%5C++%5C+%0A%3D++frac%7B3%7D%7B2%7D+%2B++frac%7B9m%5E2%2B3m+-6m%5E2%2B2m%7D%7B-%283m-1%29%283m%2B1%29%7D+%2A++frac%7B%283m-1%29%5E2%7D%7B2m%283m%2B5%29%7D+%3D+%5C++%5C+%0A%3D+frac%7B1%7D%7B2%7D+%2B++frac%7B3m%5E2%2B5m+%7D%7B-+%283m-1%29%283m%2B1%29%7D+%2A++frac%7B%283m-1%29%5E2%7D%7B2%283m%5E2%2B5m%29%7D+%3D++%5C++%5C+%0A%3D+frac%7B3m%2B1%7D%7B2%283m%2B1%29%7D+-++frac%7B2%283m-1%29%7D%7B3m%2B1+%7D+%3D++%0A%3D+++frac%7B-3m%2B3%7D%7B2%283m%2B1%29%7D+%3D+++1.5+%2A++frac%7B1-m%7D%7B3m%2B1%7D+ "frac{1}{2} + ( frac{3m}{1-3m } + frac{2m}{3m+1} ) * frac{9m^2-6m +1}{6m^2+10m} = \ \
= frac{1}{2} + frac{3m(3m+1) -2m (3m-1)}{-(3m-1)(3m+1)} * frac{(3m-1)^2}{2m(3m+5)} = \ \
= frac{3}{2} + frac{9m^2+3m -6m^2+2m}{-(3m-1)(3m+1)} * frac{(3m-1)^2}{2m(3m+5)} = \ \
= frac{1}{2} + frac{3m^2+5m }{- (3m-1)(3m+1)} * frac{(3m-1)^2}{2(3m^2+5m)} = \ \
= frac{3m+1}{2(3m+1)} - frac{2(3m-1)}{3m+1 } =
= frac{-3m+3}{2(3m+1)} = 1.5 * frac{1-m}{3m+1}")
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