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justaguide eNotes educator| Certified Educator

The equation to be solved is : 1/x - 1/(x+4) = 1/3

1/x - 1/(x+4) = 1/3

=> (x + 4) - x = x(x + 4)/3

=> 4*3 = x^2 + 4x

=> x^2 + 4x - 12 = 0

=> x^2 + 6x - 2x - 12 = 0

=> x(x + 6) - 2(x + 6) = 0

=> (x - 2)(x + 6) = 0

=> x = 2 and x = -6

The solution of the equation is x = 2 and x = -6

rosemeri | Student

1/x - 1/(x+4) = 1/3

First things first: make all the "x"s nominators as opposed to demoninators. Multiply everything by (x)(x+4) to eliminate the demoninators with "x" in them.

(1/x)(x)(x+4) - (1/(x+4))(x)(x+4) = (1/3)(x)(x+4)

reduces to: (x+4) - (x) = (x)(x+4)/3

Simplify: x + 4 - x = (x^2 + 4x)/3

Multiply by 3: 4(3) = x^2 + 4x = 12

x^2 + 4x - 12 = 0

Now we just have to find its parts. We know that there is addition and substraction because 12 is negative. 4x is positive so we know that the greater number is positive. Therefore, two factors of 12 will be subtracted to equal 4.

The factors of 12 are 12 & 1, 3 & 4, 2 & 6

The pair of 2 and 6 are the only ones that when the lesser is subtracted from the greater is 4 therefore:

(x + 6)(x - 2) = 0

x = -6, 2

I hope this helps! If you need more clarification, please post!

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