Question

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Найдите значение выражения

Answer 1

$frac{a}{5a-1} : frac{ a^{2} }{25 a^{2}-10a+1 }= frac{a}{5a-1}* frac{(5a-1) ^{2} }{ a^{2} }= frac{5a-1}{a} \\ frac{5* frac{1}{6}-1 }{ frac{1}{6} }= frac{ frac{5}{6}-1 }{ frac{1}{6} }= frac{- frac{1}{6} }{ frac{1}{6} }=-1$

$frac{a}{4a-1} : frac{ a^{2} }{16 a^{2}-8a+1 } = frac{a}{4a-1}* frac{(4a-1) ^{2} }{ a^{2} }= frac{4a-1}{a}\\ frac{4* frac{1}{7}-1 }{ frac{1}{7} }= frac{ frac{4}{7}-1 }{ frac{1}{7} }= frac{ frac{3}{7} }{ frac{1}{7} }= frac{3*7}{7*1} =3$

$frac{a}{9a-1} : frac{ a^{2} }{81 a^{2} -18a+1}= frac{a}{9a-1}* frac{(9a-1) ^{2} }{ a ^{2} }= frac{9a-1}{a}\\ frac{9* frac{1}{6}-1 }{ frac{1}{6} }= frac{ frac{9}{6} -1}{ frac{1}{6} }= frac{- frac{1}{2} }{ frac{1}{6} }=- frac{1*6}{2*1}=-3$