SOLUTION: Solve (n)/(n-3)+n=(7n-15)/(n-3)

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Question 151730: Solve (n)/(n-3)+n=(7n-15)/(n-3)
Answer by jim_thompson5910(28598) About Me  (Show Source):
You can put this solution on YOUR website!
%28n%29%2F%28n-3%29%2Bn=%287n-15%29%2F%28n-3%29 Start with the given equation.


Multiply every term on both sides by the LCD n-3. Doing this will eliminate all of the fractions.



n%2Bn%28n-3%29=7n-15 Simplify


n%2Bn%5E2-3n=7n-15 Distribute


n%2Bn%5E2-3n-7n%2B15=0 Subtract 7n from both sides. Add 15 to both sides.


n%5E2-9n%2B15=0 Combine like terms.


Notice we have a quadratic equation in the form of an%5E2%2Bbn%2Bc where a=1, b=-9, and c=15


Let's use the quadratic formula to solve for n


n+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


n+=+%28-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%281%29%2815%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-9, and c=15


n+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%281%29%2815%29+%29%29%2F%282%281%29%29 Negate -9 to get 9.


n+=+%289+%2B-+sqrt%28+81-4%281%29%2815%29+%29%29%2F%282%281%29%29 Square -9 to get 81.


n+=+%289+%2B-+sqrt%28+81-60+%29%29%2F%282%281%29%29 Multiply 4%281%29%2815%29 to get 60


n+=+%289+%2B-+sqrt%28+21+%29%29%2F%282%281%29%29 Subtract 60 from 81 to get 21


n+=+%289+%2B-+sqrt%28+21+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


n+=+%289%2Bsqrt%2821%29%29%2F%282%29 or n+=+%289-sqrt%2821%29%29%2F%282%29 Break up the expression.


So our answers are n+=+%289%2Bsqrt%2821%29%29%2F%282%29 or n+=+%289-sqrt%2821%29%29%2F%282%29


which approximate to n=6.791 or n=2.209