SOLUTION: Solve: [n/(n-4)]+n=(12-4n)/(n-4). Thank you

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Question 42123: Solve: [n/(n-4)]+n=(12-4n)/(n-4).
Thank you
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
n%2F%28n-4%29%2Bn=%2812-4n%29%2F%28n-4%29
or %28n+%2B+n%28n-4%29%29%2F%28n-4%29=%2812-4n%29%2F%28n-4%29
or %28n+%2B+n%5E2-4n%29%2F%28n-4%29=%2812-4n%29%2F%28n-4%29
or n%5E2-3n=12-4n
[when 'n' not equal to 4; as otherwise division by (n-4) is division by 0 which is undefined]
or n%5E2%2Bn-12=0

Using the quadratic formula
n+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-12%29+%29%29%2F%282%2A1%29+
or n+=+%281+%2B-+sqrt%28+49+%29%29%2F2+
or n+=+%281+%2B-+7%29%2F2+

Therefore either n = 4 or n = -3.
Now, we have already seen that the equation is not valid for n = 4.
So the only solution is n = -3.