Question

Помогите пожалуйста)))

Answer 1

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

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