Solving the equation by using the LCD?!?!

1/x=1/2+2/x

Please show steps!
Thanks!!(:

1/x=1/2+2/x

isolate x to get all x terms on one side

1/x - 2/x=1/2

combine like terms

-1/x=1/2

1/x=-1/2

cross multiply

-x=2

x=-2

1/x = 1/2 + 2/x

Multiply both sides by 2x, : 2 = x + 4

x = 2 -4 = -2 >=======================< ANSWER

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