\\
t\neq0;\\
2t^2-3t-2=0\\t= \frac{3^+_-\sqrt{9+16}}{4} =\frac{3^+_-5}{4}\\
t=2=>log_3(x+1)=2;\\x+1=3^2;\\x=8\\\\t=-1/2=>log_3(x+1)=-1/2;\\x+1= \frac{1}{\sqrt3} ;\\x=\frac{1}{\sqrt3}-1" alt="3+2log_{x+1}3=2log_3(x+1)\\
2(log_3(x+1)-\frac{1}{log_3(x+1)})-3=0\\
(t=log_3(x+1))\\
2(t-1/t)-3=0\\
\frac{2t^2-3t-2}{t} =0=>\\
t\neq0;\\
2t^2-3t-2=0\\t= \frac{3^+_-\sqrt{9+16}}{4} =\frac{3^+_-5}{4}\\
t=2=>log_3(x+1)=2;\\x+1=3^2;\\x=8\\\\t=-1/2=>log_3(x+1)=-1/2;\\x+1= \frac{1}{\sqrt3} ;\\x=\frac{1}{\sqrt3}-1" align="absmiddle" class="latex-formula">