Ответ: x = -9
Пошаговое объяснение:
![log_9(x^2+x)=log_9(x^2-9) log_9(x^2+x)=log_9(x^2-9)](https://tex.z-dn.net/?f=log_9%28x%5E2%2Bx%29%3Dlog_9%28x%5E2-9%29)
ОДЗ
0}\atop{x^2-9>0}}\right.\\\left\{{{x(x+1)>0}\atop{(x-3)(x+3)>0}}\right.\\\left\{{{x>0|x<-1}\atop{x>3|x<-3}}\right." alt="\left\{{{x^2+x>0}\atop{x^2-9>0}}\right.\\\left\{{{x(x+1)>0}\atop{(x-3)(x+3)>0}}\right.\\\left\{{{x>0|x<-1}\atop{x>3|x<-3}}\right." align="absmiddle" class="latex-formula">
x ∈ (-∞; -3) ∪ (3; +∞)
![x^2+x=x^2-9\\x=-9 x^2+x=x^2-9\\x=-9](https://tex.z-dn.net/?f=x%5E2%2Bx%3Dx%5E2-9%5C%5Cx%3D-9)
x = -9 удовлетворяет ОДЗ.