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

[latex] \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 } [/latex] [latex]\left( \dfrac{a}{b} + \dfrac{b}{a} -2\right)\cdot\dfrac{1}{a-b} = \left( \dfrac{a^2}{ab} + \dfrac{b^2}{ab} - \dfrac{2ab}{ab} \right)\cdot\dfrac{1}{a-b} = \\\\ = \dfrac{a^2+b^2-2ab}{ab}\cdot\dfrac{1}{a-b} = \dfrac{(a-b)^2}{ab}\cdot\dfrac{1}{a-b} = \dfrac{(a-b)^2}{ab(a-b)} = \dfrac{a-b}{ab} [/latex] [latex]\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} [/latex]