SOLUTION: 1/8 - 3/5 = 1/x Solve for x?

Question 136044: 1/8 - 3/5 = 1/x Solve for x?
Answer by JSmall(7) (Show Source): You can put this solution on YOUR website!
1/8 - 3/5 = 1/x Solve for x?
The simplest way to solve this is to start by subtracting the fractions:
1/8 - 3/5
The least common denominator of 8 and 5 is 40. 1/8 = 5/40 and 3/5 = 24/40 giving
5/40 - 24/40
which is
-19/40
Now the equation is:
-19/40 = 1/x
Perhaps you can intuitively tell that if 1/x = -19/40 that x/1 (or x) = -40/19. If this is not obvious, then just multiply both sides by the product of the two denominators: 40x
On the left side the 40's cancel leaving -19x and on the right side the x's cancel leaving 40. Now we have:
-19x = 40
Dividing by -19 we get:
x = -40/19
which, as a mixed number, is:
x = -2 2/19
Another solution would be to start by eliminating all the fractions. This can be done by multiplying both sides of the equation by the least common denominator (LCD) of all three denominators.
For these denominators the LCD is (8)(5)(x).
So the fractions can be eliminated by multiplying both sides of the equation by (8)(5)(x).
(8)(5)(x)(1/8 - 3/5) = (8)(5)(x)(1/x)
When 1/8 is multiplied by (8)(5)(x), the 8's cancel leaving (5)(x)(1) which is 5x.
When 3/5 is multiplied by (8)(5)(x), the 5's cancel leaving (8)(x)(3) which is 24x
When 1/x is multiplied by (8)(5)(x), the x's cancel leaving (8)(5)(1) which is 40.
Now the equation is:
5x - 24x = 40
Subtracting we get:
-19x = 40
Dividing by -19 we get:
x = -40/19
Converting to a mixed number we get:
x = -2 2/19
The second procedure may be a little more complicated. But it is useful for similar, more complicated problems like:
1/3 - 1/x = 2/(1+x)
1/3 and 1/x can be subtracted (and a solution found in the same way as the first solution above) but it may not be as easy as subtracting "variable-less" fractions like 1/8 and 3/5. The second procedure may be easier and more generally useful.

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