SOLUTION: I am TOTALLY lost on this one :( PLEASE HELP!! All of the fractions really confuse me. I'm supposed to solve for x... 2/3 + 1/(2 2/5) - 1/x = 1/3

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Question 456296: I am TOTALLY lost on this one :( PLEASE HELP!! All of the fractions really confuse me. I'm supposed to solve for x...

2/3 + 1/(2 2/5) - 1/x = 1/3 - 1/(2 2/3)

Found 2 solutions by ptaylor, Alan3354:
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
OK
I'm assuming that 2 2/5=2 and 2/5ths and that 2 2/3=2 and 2/3rds
First 2 2/5=12/5
and
2 2/3=8/3
Now lets rewrite the equation:
2/3 + 1/(12/5)-1/x=1/(8/3)
Next, 1/(12/5)=5/12 (multiply numerator and denominator by 5/12)
and
1/(8/3)=3/8
Lets now rewrite the equation again:
2/3 + 5/12 - 1/x=3/8 subtract 2/3 and also 5/12 from each side of the equation:
-1/x=3/8-2/3-5/12 or
-1/x=9/24-16/24-10/24 combine like terms
-1/x=-2/24 cross multiply
-2x=-24
x=12--------------ans
Hope this helps--ptaylor

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
2/3 + 1/(2 2/5) - 1/x = 1/3 - 1/(2 2/3)
2/3 + 1/(12/5) - 1/x = 1/3 - 1/(8/3)
2/3 + 5/12 - 1/x = 1/3 - 3/8
8/12 + 5/12 - 1/x = 8/24 - 9/24
13/12 - 1/x = -1/24
26/24 - 1/x = -1/24
-1/x = -27/24
1/x = 27/24
x = 24/27
x = 8/9

SOLUTION: I am TOTALLY lost on this one :( PLEASE HELP!! All of the fractions really confuse me. I'm supposed to solve for x... 2/3 + 1/(2 2/5) - 1/x = 1/3 - 1/(2 2/3)