SOLUTION: (6/n^2) - (1/n) = -(1/3n) I know the LCM is 3n^2 but I'm still confused. Thanks

Algebra ->  Rational-functions -> SOLUTION: (6/n^2) - (1/n) = -(1/3n) I know the LCM is 3n^2 but I'm still confused. Thanks      Log On


   

Question 1019520: (6/n^2) - (1/n) = -(1/3n)
I know the LCM is 3n^2 but I'm still confused. Thanks
Found 2 solutions by josmiceli, robertb:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%286%2Fn%5E2%29+-+%281%2Fn%29+=+-%28+1%2F%283n%29+%29+
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Just multiply both sides by +3n%5E2+
I'll do it step by step:
+3n%5E2%2A%28+6%2Fn%5E2+%29+-+3n%5E2%2A%28+1%2Fn+%29+=+3n%5E2%2A%28+-1%2F%283n%29+%29+
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I'll rearrange
+%28+n%5E2%2Fn%5E2+%29%2A18+-+%28+n%5E2%2Fn+%29%2A3+=+%28+n%5E2%2Fn+%29%2A%28-1%29+
+18+-+3n+=+%28-1%29%2An+
+18+-+3n+%2B+n+=+0+
+18+-+2n+=+0+
+2n+=+18+
+n+=+9+
Check:
+%286%2Fn%5E2%29+-+%281%2Fn%29+=+-%28+1%2F%283n%29+%29+
+%286%2F9%5E2%29+-+%281%2F9%29+=+-%28+1%2F%283%2A9%29+%29+
+6%2F81+-+9%2F81++=+-1%2F27+
+6%2F81+-+9%2F81+=+-3%2F81+
+-3%2F81+=+-3%2F81+
OK

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the denominators present in every rational expression, namely n%5E2, n, and 3n. To find the LCD, find the highest power of any distinct factors appearing, and then multiply them together.
One factor is the number 3, whose highest power is 1. (So 3%5E1, or 3, appears in the LCD). The factors n and n%5E2 also appear, both of them powers of the same base n. So choose n%5E2, because it is the highest power of n appearing.
The LCD is then 3n%5E2.