Question

помогите пожалуйста ​

Answer 1

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

$\bigg(\dfrac{a^2}{a+5}-\dfrac{a^3}{(a+5)^2}\bigg):\bigg(\dfrac a{a+5}-\dfrac{a^2}{(a-5)(a+5)}\bigg)=\dfrac{5a-a^2}{a+5}$

$\dfrac{a^2(a+5)-a^3}{(a+5)^2}:\dfrac{a(a-5)-a^2}{(a-5)(a+5)}=\dfrac{5a-a^2}{a+5}$

$\dfrac{a^3+5a^2-a^3}{(a+5)^2}\cdot\dfrac{(a-5)(a+5)}{a^2-5a-a^2}=\dfrac{5a-a^2}{a+5}$

$\dfrac{5a^2}{a+5}\cdot\dfrac{a-5}{-5a}=\dfrac{5a-a^2}{a+5}$

$\dfrac{a(a-5)}{-(a+5)}=\dfrac{5a-a^2}{a+5}$

$\dfrac{-a(a-5)}{a+5}=\dfrac{5a-a^2}{a+5}$

$\dfrac{a(5-a)}{a+5}=\dfrac{5a-a^2}{a+5}$

$\dfrac{5a-a^2}{a+5}=\dfrac{5a-a^2}{a+5}$

Тождество верно