Question

Which vaule(s) of x are soulution(s) of the equation below

Answer 1

`\begin{gathered} (1)/(x-4)+(x)/(x-2)=(2)/(x^2-6x+8) \\ Add\text{ing} \\ (1)/(x-4)+(x)/(x-2)=((1)(x-2)+(x-4)(x))/((x-4)(x-2))=((x-2)+(x-4)(x))/((x-4)(x-2)) \\ Factor\text{ing} \\ (2)/(x^2-6x+8)=(2)/((x-4)(x-2)) \\ ((x-2)+(x-4)(x))/((x-4)(x-2))=(2)/((x-4)(x-2)) \\ (x-2)+(x-4)(x)=2 \\ x-2+x^2-4x=2 \\ x^2-3x-2=2 \\ x^2-3x-2-2=0 \\ x^2-3x-4=0 \\ (x-4)(x+1)=0 \\ x-4=0 \\ x=4 \\ x+1=0 \\ x=-1 \\ \text{The solution is x=4 and x=-1} \end{gathered}`