SOLUTION: please help with this if 2x=3y=6z then what will be value of 1/x + 1/y + 1/z

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Question 190049: please help with this
if 2x=3y=6z
then what will be value of
1/x + 1/y + 1/z
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Break up the equation
(1) 2x+=+3y
(2) 3y+=+6z
From (1)
x+=+%283%2F2%29%2Ay
From (2)
6z+=+3y
z+=+%281%2F2%29%2Ay
----------------
1%2Fx+%2B+1%2Fy+%2B+1%2Fz
1%2F%28%283%2F2%29%2Ay%29+%2B+1%2Fy+%2B+1%2F%28%281%2F2%29%2Ay%29
Multiply by 2%2F2
%282%2F2%29%2A%281%2F%28%283%2F2%29%2Ay%29+%2B+1%2Fy+%2B+1%2F%28%281%2F2%29%2Ay%29%29

2%2F%283y%29+%2B+2%2F%282y%29+%2B+2%2Fy+
4%2F%286y%29+%2B+6%2F%286y%29+%2B+12%2F%286y%29
22%2F%286y%29
(1) 11%2F%283y%29
and since y+=+2z
(2) 11%2F%286z%29
And since y+=+%282%2F3%29%2Ax
(3) 11%2F%284x%29
(1),(2), and (3) are answers