SOLUTION: when the reciprocal of three times a number is subtracted from the reciprocal of the number the result is one sixth find the number

Question 563687: when the reciprocal of three times a number is subtracted from the reciprocal of the number the result is one sixth find the number
Found 2 solutions by jlshires, ScrewYouScience:
Answer by jlshires(17) (Show Source): You can put this solution on YOUR website!
The first step is to let x=the number
The reciprocal of three times a number.. three times the number would be 3x, the reciprocal of that is 1/3x
That is being subtracted from the reciprocal of the number (1/x)
The first part of the equation is:
(1/x)-(1/3x)
The result is 1/6 Therefore:
(1/x)-(1/3x)=1/6
In order to subtract two fractions, they need to have the same denominator, or bottom number. You can achieve this by multiplying the first number by 3
3(1/x)-(1/3x)=1/6 this will give you
(3/3x)-(1/3x)=1/6
subtraction in fractions is really a subtraction of the numerators over the denominator (because the denominators are the same) so this is equal to
(3-1)/3x=1/6 or 2/3x=1/6
Now you can cross multiply to get
2(6)=(3x)(1) or 12=3x
divide both sides of the equation by 3 and you will get
x=4
Answer by ScrewYouScience(2) (Show Source): You can put this solution on YOUR website!
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