Solve the rational equation below.

Question

1/x-2+ 2x/(x-2)(x-8)=x/2(x-8)

Answer 1

You were missing a bracket, should be
1/(x-2) + 2x/(x-2)(x-8)=x/2(x-8)

multiply each term by 2(x-2)(x-8) , the LCD
2(x-8) + 4x = x(x-2)
2x - 16 + 4x = x^2 - 2x
x^2 -8x + 16 = 0
(x-4)^2 = 0
x-4 = 0
x = 4

check:
LS = 1/2 + 8/(2)(-4)
= 1/2 - 1 = -1/2
RS = 4/(-8) = -1/2