Simplify the fraction (1/(3+x)-1/3)/x?

First, we'll perform the subtraction from numerator. To
subtract the given fractions they must have the same
denominator.

1/(3+x) - 1/3 = [3 -
(3+x)]/3(3+x)

We'll remove the
brackets:

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

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

Now, we'll re-write the
fraction:

[1/(3+x) - 1/3]/x =
-x/3x(3+x)

We'll simplify and we'll
get:

[1/(3+x) - 1/3]/x = -1/(9 +
3x)

The simplified fraction is -1/(9 +
3x).