Упростите выражение. Алгебра 8 класс
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Ответил m11m
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1) ![frac{a}{a-7}- frac{2a}{a^2-14a+49}= frac{a}{a-7}- frac{2a}{(a-7)^2}= frac{a(a-7)-2a}{(a-7)^2}= \
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= frac{a^2-7a-2a}{(a-7)^2}= frac{a^2-9a}{(a-7)^2}= frac{a(a-9)}{(a-7)^2}](https://tex.z-dn.net/?f=+frac%7Ba%7D%7Ba-7%7D-++frac%7B2a%7D%7Ba%5E2-14a%2B49%7D%3D+frac%7Ba%7D%7Ba-7%7D-+frac%7B2a%7D%7B%28a-7%29%5E2%7D%3D+frac%7Ba%28a-7%29-2a%7D%7B%28a-7%29%5E2%7D%3D+%5C+%0A+%5C+%0A%3D+frac%7Ba%5E2-7a-2a%7D%7B%28a-7%29%5E2%7D%3D+frac%7Ba%5E2-9a%7D%7B%28a-7%29%5E2%7D%3D+frac%7Ba%28a-9%29%7D%7B%28a-7%29%5E2%7D++++++++ "frac{a}{a-7}- frac{2a}{a^2-14a+49}= frac{a}{a-7}- frac{2a}{(a-7)^2}= frac{a(a-7)-2a}{(a-7)^2}= \
\
= frac{a^2-7a-2a}{(a-7)^2}= frac{a^2-9a}{(a-7)^2}= frac{a(a-9)}{(a-7)^2}")
2)![frac{49-a^2}{a-9} * frac{a(a-9)}{(a-7)^2} = frac{-(a-7)(a+7)}{a-9}* frac{a(a-9)}{(a-7)^2}= \
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= frac{-(a+7)*a}{a-7} = frac{-a^2-7a}{a-7}](https://tex.z-dn.net/?f=+frac%7B49-a%5E2%7D%7Ba-9%7D+%2A++frac%7Ba%28a-9%29%7D%7B%28a-7%29%5E2%7D+%3D+frac%7B-%28a-7%29%28a%2B7%29%7D%7Ba-9%7D%2A+frac%7Ba%28a-9%29%7D%7B%28a-7%29%5E2%7D%3D+%5C+%0A+%5C+%0A%3D+frac%7B-%28a%2B7%29%2Aa%7D%7Ba-7%7D+%3D+frac%7B-a%5E2-7a%7D%7Ba-7%7D++++++ "frac{49-a^2}{a-9} * frac{a(a-9)}{(a-7)^2} = frac{-(a-7)(a+7)}{a-9}* frac{a(a-9)}{(a-7)^2}= \
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= frac{-(a+7)*a}{a-7} = frac{-a^2-7a}{a-7}")
3)![frac{-a^2-7a}{a-7}+ frac{14a}{a-7}= frac{-a^2-7a+14a}{a-7}= frac{-a^2+7a}{a-7}= \
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= frac{-a(a-7)}{a-7}= -a](https://tex.z-dn.net/?f=+frac%7B-a%5E2-7a%7D%7Ba-7%7D%2B+frac%7B14a%7D%7Ba-7%7D%3D+frac%7B-a%5E2-7a%2B14a%7D%7Ba-7%7D%3D+frac%7B-a%5E2%2B7a%7D%7Ba-7%7D%3D+%5C+%0A+%5C+%0A%3D+frac%7B-a%28a-7%29%7D%7Ba-7%7D%3D+-a+++++ "frac{-a^2-7a}{a-7}+ frac{14a}{a-7}= frac{-a^2-7a+14a}{a-7}= frac{-a^2+7a}{a-7}= \
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= frac{-a(a-7)}{a-7}= -a")
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