Question

докажите тождество! !!!8 кдасс срочно

Answer 1

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