You can put this solution on YOUR website! From (x-6)/4-(x-4)/6=1-x/10 we can multiply by the LCD and clear all the fractions in one step...here the LCD is 60...so multiply everything by 60 and get...
15(x-6) - 10(x-4) = 60 - 6x
15x - 90 - 10x + 40 = 60 - 6x
Collect like terms and solve
5x - 50 = 60 - 6x
11x = 110
x = 10