[tex]Domain:\\\\1+m\neq0\to m\neq-1\\\\\dfrac{1-m}{1+m}=\dfrac{2}{3}\qquad\text{cross multiply}\\\\3(1-m)=2(1+m)\qquad\text{use distributive property}\\\\(3)(1)+(3)(-m)=(2)(1)+(2)(m)\\\\3-3m=2+2m\qquad\text{subtract 3 from both sides}\\\\-3m=-1+2m\qquad\text{subtract 2m from both sides}\\\\-5m=-1\qquad\text{divide both sides by (-5)}\\\\m=\dfrac{1}{5}\neq-1\\\\Answer:\ \boxed{m=\dfrac{1}{5}}[/tex]
