[tex](x-3)^{2} =(x+2)\cdot (x-3)\\\\x^{2} -6x+9=x^{2} -3x+2x-6\\\\x^{2} -6x+9=x^{2} -x-6\\\\-6x+x=-6-9\\\\-5x=-15~~\mid \div (-5)\\\\x=3[/tex]
[tex]\dfrac{x-2}{3} -\dfrac{4-x}{2} <\dfrac{5}{6} ~~\mid \cdot 6\\\\2\cdot (x-2)-3\cdot (4-x)<5\\\\2x-4-12+3x<5\\\\5x<5+16\\\\5x< 21~~\mid \div 5\\\\x<\dfrac{21}{5} \\\\x<4\dfrac{1}{5} ~~\Rightarrow ~~x\in (-\infty ,4\dfrac{1}{5})[/tex]
