Question

Упростите выражение.
Даю 100 балов​

Answer 1

Ответ:

$1)\ \ \displaystyle \Big(\frac{a+2}{a-2}+\frac{a-2}{a+2}\Big):\frac{a^2+4}{4-a^2}=\frac{(a+2)^2+(a-2)^2}{(a-2)(a+2)}\cdot \frac{(2-a)(2+a)}{a^2+4}=\\\\\\=\frac{a^2+4a+4+a^2-4a+4}{(a-2)(a+2)}\cdot \frac{-(a-2)(a+2)}{a^2+4}=\\\\\\=-\frac{2\, (a^2+4)}{a^2+4}=-2$

$2)\ \ \displaystyle \Big(\frac{a^2}{a+5}-\frac{a^3}{a^2+10a+25}\Big):\Big(\frac{a}{a+5}-\frac{a^2}{a^2-25}\Big)=\\\\\\=\Big(\frac{a^2}{a+5}-\frac{a^3}{(a+5)^2}\Big):\Big(\frac{a}{a+5}-\frac{a^2}{(a-5)(a+5)}\Big)=\\\\\\=\frac{a^2(a+5)-a^3}{(a+5)^2}:\frac{a(a-5)-a^2}{(a-5)(a+5)}=\frac{5a^2}{(a+5)^2}\cdot \frac{(a-5)(a+5)}{-5a}=\\\\\\=-\frac{a(a-5)}{a+5}=\frac{a(5-a)}{a+5}$

Answer 2

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