Solve: \[ 6\left(\cfrac{x-2}{x-6}\right)+\cfrac{x-2}{x+2}=1 \quad [x\ne -2,6] \]

Q.Solve: \[ 6\left(\cfrac{x-2}{x-6}\right)+\cfrac{x-2}{x+2}=1 \quad [x\ne -2,6] \]

\[ 6\left(\cfrac{x-2}{x-6}\right)+\cfrac{x-2}{x+2}=1 \] \[ \text{or, } \cfrac{6(x-2)}{x-6}=1-\cfrac{x-2}{x+2} \] \[ \text{or, } \cfrac{6(x-2)}{x-6}=\cfrac{x+2-x+2}{x+2} \] \[ \text{or, } \cfrac{6(x-2)}{x-6}=\cfrac{4}{x+2} \] \[ \text{or, } \cfrac{3(x-2)}{x-6}=\cfrac{2}{x+2} \] \[ \text{or, } 3(x^2-4)=2(x-6) \] \[ \text{or, } 3x^2-12-2x+12=0 \] \[ \text{or, } 3x^2-2x=0 \] \[ \text{or, } x(3x-2)=0 \] \[ \therefore \text{ either } x=0 \] \[ \text{or, } 3x-2=0 \text{ or } x=\cfrac{2}{3} \] \[ \therefore \text{ The solution is } x=0 \text{ or } \cfrac{2}{3} \quad \textbf{(Answer)} \]