0 \wedge x-2>0 \wedge x+2>0\\ x>1 \wedge x>2 \wedge x>-2\\ x>2\\ \lg(x-1)(x-2)=\lg(x+2)\\ x^2-2x-x+2=x+2\\ x^2-4x=0\\ x(x-4)=0\\ x=0 \vee x=4\\ 0\not>2\\ \boxed{x=4}" alt="\\\lg(x-1)+\lg(x-2)=\lg(x+2) \\ x-1 >0 \wedge x-2>0 \wedge x+2>0\\ x>1 \wedge x>2 \wedge x>-2\\ x>2\\ \lg(x-1)(x-2)=\lg(x+2)\\ x^2-2x-x+2=x+2\\ x^2-4x=0\\ x(x-4)=0\\ x=0 \vee x=4\\ 0\not>2\\ \boxed{x=4}" align="absmiddle" class="latex-formula">