Question

докажите тождество! !!!8 кдасс срочно

Answer 1

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