Question

Помогите пожалуйста)))

Answer 1

$frac{1}{x+3}-frac{1}{x+9}=frac{1}{x+5}-frac{1}{x+21}\\frac{x+9-x-3}{(x+3)(x+9)}=frac{x+21-x-5}{(x+5)(x+21)}\\frac{6}{(x+3)(x+9)}=frac{16}{(x+5)(x+21)}\\xneq-3;xneq -9;xneq-5;xneq-21\\6(x+5)(x+21)=16(x+3)(x+9)\\3(x^{2}+21x+5x+105)=8(x^{2}+9x+3x+27)\\8x^{2}+96x+216-3x^{2}-78x-315=0\\5x^{2}+18x-99=0$

$D=18^{2}-4*5*(-99)=324+1980=2304=48^{2}\\x_{1}=frac{-18+48}{10}=3\\x_{2}=frac{-18-48}{10}=-6,6$