Question

ДАЮ 20 БАЛЛОВ!
Упростите выражения:
а)$frac{4a}{ a^{2} -64b ^{2} } - frac{4}{a+8b}$
б)$( frac{a}{b} + frac{b}{a} -2)* frac{1}{a-b}$
в)$( frac{9y}{x} - frac{49x}{y} ):(3y-7x)$

Answer 1

$dfrac{4a}{ a^{2} -64b ^{2} } - dfrac{4}{a+8b} = dfrac{4a}{ a^2-64b^2 } - dfrac{4(a-8b)}{(a+8b)(a-8b)} = \\ = dfrac{4a}{ a^2-64b^2 } - dfrac{4(a-8b)}{a^2-64b^2} = dfrac{4a-4(a-8b)}{ a^2-64b^2 } = \\ = dfrac{4a-4a+32b}{ a^2-64b^2 } = dfrac{32b}{ a^2-64b^2 }$

$left( dfrac{a}{b} + dfrac{b}{a} -2right)cdotdfrac{1}{a-b} = left( dfrac{a^2}{ab} + dfrac{b^2}{ab} - dfrac{2ab}{ab} right)cdotdfrac{1}{a-b} = \\ = dfrac{a^2+b^2-2ab}{ab}cdotdfrac{1}{a-b} = dfrac{(a-b)^2}{ab}cdotdfrac{1}{a-b} = dfrac{(a-b)^2}{ab(a-b)} = dfrac{a-b}{ab}$
$left( dfrac{9y}{x} - dfrac{49x}{y} right):(3y-7x)= left( dfrac{9y^2}{xy} - dfrac{49x^2}{xy} right)cdot dfrac{1}{3y-7x} = \\ = dfrac{9y^2-49x^2}{xy} cdot dfrac{1}{3y-7x} = dfrac{(3y-7x)(3y+7x)}{xy} cdot dfrac{1}{3y-7x} = \\ =dfrac{(3y-7x)(3y+7x)}{xy(3y-7x)} =dfrac{3y+7x}{xy}$

Answer 2

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