Question

Which value(s) of x are solution(s) of the equation below

Answer 1

`(1)/(x - 4) + (x)/(x - 2) = \frac{2}{ {x}^(2) - 6x + 8} \\ \\ (1)/(x - 4) + (x)/(x - 2) = (2)/((x - 4)(x - 2)) \\ \\ ((x - 2) + x(x - 4))/((x - 4)(x - 2)) = (2)/((x - 4)(x - 2)) \\ \\ x - 2 + {x }^(2) - 4x = 2 \\ \\ {x}^(2) - 3x - 4 = 0 \\ (x - 4)(x + 1) = 0 \\ x = 4 \: \: and \: \: x = - 1`

Answer 2

x =-1 , x=4

Explanation:

`(1)/(x-4)+(x)/(x-2)=(2)/(x^2-6x+8)\\\\\mathrm{Multiply\:by\:LCM=}\left(x-4\right)\left(x-2\right)\\\\(1)/(x-4)\left(x-4\right)\left(x-2\right)+(x)/(x-2)\left(x-4\right)\left(x-2\right)=(2)/(x^2-6x+8)\left(x-4\right)\left(x-2\right)\\\\Simplify\\\\x-2+x\left(x-4\right)=2\\\\Solve\\\\x=4,\:x=-1`