Задача 74157 Сократить уравнение...

6558cdf4b16b5471ac0a9e96

11/18/2023 2:46:57 PM

Сократить уравнение

5f3ea7e3faf909182968ddd9

11/18/2023 7:59:02 PM

★

[m](\frac{a}{a-5}-\frac{a}{a+5}-\frac{a+25}{25-a^2})\cdot\frac{a-5}{a^2+10a+25}=[/m]


1)
[m](\frac{a}{a-5}-\frac{a}{a+5}-\frac{a+25}{25-a^2})=(\frac{a}{a-5}-\frac{a}{a+5}+\frac{a+25}{a^2-25})=[/m]

[m]=(\frac{a(a+5)}{(a-5)(a+5)}-\frac{a(a-5)}{(a+5)(a-5)}+\frac{a+25}{(a-5)(a+5)})=\frac{a(a+5)-a(a-5)+a+25}{(a-5)(a+5)}=\frac{a^2+5a-a^2+5a+a+25}{(a-5)(a+5)}=\frac{11a+25}{(a-5)(a+5)}[/m]


2)
[m]\frac{11a+25}{(a-5)(a+5)}\cdot\frac{a-5}{a^2+10a+25}=\frac{(11a+25)(a-5)}{(a-5)(a+5)(a+5)^2}=\frac{11a+25}{(a+5)^3}[/m]