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Express in simplest form

3n/n^2-49 - 2/3n+21

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)

3n/(n^2-49) - 2/(3n+21) <==Is this what you want?

LCD = 3(n+7)(n-7)

3n/(n^2-49) - 2/(3n+21)

= (9n - 2(n-7))/LCD

= (7n + 14)/LCD

= 7(n+2)/[3(n+7)(n-7)] <==Answer

Patricia M. | Strong in both Math and English plus Test Prep (ACT,SAT,ASVAB,GED...)Strong in both Math and English plus Tes...
4.9 4.9 (174 lesson ratings) (174)

Let me be sure about the format of this expression before I give you a solution, because it will definitely make a difference! May I take this expression literally, as it is written? Or is it actually a difference of two fractions... in other words,  with 3n being the numerator of the first fraction, n-squared minus 49 the denominator of the first fraction; 2 being the numerator of the second fraction, and 3n+21 the denominator of the second fraction?  That would make it: 3n/(n^2-49) - 2/(3n+21).

If you are studying order of operations, your original format makes sense. If you are studying factoring, the  alternate format I described would make more sense. 

Note: I didn't notice earlier that Robert J. has answered, making the same assumption that I have... your solution is there.