Question

7. Задание 7 № 31 1473. Упростите выражение
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Answer 1

$\displaystyle \tt \frac{b}{a^2+ab}\div\frac{b^2}{a^2-b^2}=\frac{b}{a(a+b)}\cdot\frac{(a-b)(a+b)}{b^2}=\frac{1}{a}\cdot\frac{a-b}{b}=\bold{\frac{a-b}{ab}}\\\\\\ \displaystyle \tt \frac{a-b}{ab}=\frac{(\sqrt{5}-1)-(\sqrt{5}+1)}{(\sqrt{5}-1)(\sqrt{5}+1)}=\frac{\sqrt{5}-1-\sqrt{5}-1}{5-1}=\frac{-2}{4}=-\frac{1}{2}=\boxed{\bold{-0,5}}$

ОТВЕТ: $\displaystyle \tt -0,5$