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

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!