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

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We have to simplify (1/(3+x)-1/3)/x

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

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

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

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

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

**The simplified expression is -1/3*(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).**

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