Homework Help

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

user profile pic

gmaxim | Student, College Freshman | (Level 1) eNoter

Posted July 29, 2011 at 2:27 AM via web

dislike 0 like

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

2 Answers | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 29, 2011 at 2:30 AM (Answer #1)

dislike 0 like

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)

user profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted July 29, 2011 at 2:32 AM (Answer #2)

dislike 0 like

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).

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes