8. Упростить выражения: 1) (1/a + 1/b)^2 : (1/a^2 − 1/b^2); 2) (1/(m − n) − 1/(m + n)) · 2/(3m − 3n); 3) a/(a + 1) − a/(a − 5); 4) (x^2 − y^2)/(xy) : (x − y)/(3y) · (x + y)/(x + y).

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Вопрос:

Accepted Answer

\[\left(\frac1a+\frac1b\right)^2:\left(\frac1{a^2}-\frac1{b^2}\right)=\frac{(a+b)^2}{a^2b^2}:\frac{b^2-a^2}{a^2b^2}=\frac{(a+b)^2}{(b-a)(a+b)}=\frac{a+b}{b-a}.\]
\[\left(\frac1{m-n}-\frac1{m+n}\right)\cdot\frac2{3m-3n}=\frac{2n}{m^2-n^2}\cdot\frac2{3(m-n)}=\frac{4n}{3(m-n)^2(m+n)}.\]
\[\frac a{a+1}-\frac a{a-5}=\frac{a(a-5)-a(a+1)}{(a+1)(a-5)}=\frac{-6a}{(a+1)(a-5)}.\]
\[\frac{x^2-y^2}{xy}:\frac{x-y}{3y}\cdot\frac{x+y}{x+y}=\frac{(x-y)(x+y)}{xy}\cdot\frac{3y}{x-y}\cdot1=\frac{3(x+y)}x.\]

Ответ: