SOLUTION: Hi. Perform the indicated operations and simplify: 2/n+2 + 1/n + n+6/n^2+2n

Algebra ->  Equations -> SOLUTION: Hi. Perform the indicated operations and simplify: 2/n+2 + 1/n + n+6/n^2+2n      Log On


   

Question 190453: Hi.
Perform the indicated operations and simplify:
2/n+2 + 1/n + n+6/n^2+2n
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28n%2B2%29+%2B+1%2Fn+%2B+%28n%2B6%29%2F%28n%5E2%2B2n%29 Start with the given expression.


2%2F%28n%2B2%29+%2B+1%2Fn+%2B+%28n%2B6%29%2F%28n%28n%2B2%29%29 Factor the last denominator


Take note that the LCD is n%28n%2B2%29


%282%2An%29%2F%28n%2A%28n%2B2%29%29+%2B+1%2Fn+%2B+%28n%2B6%29%2F%28n%28n%2B2%29%29 Multiply the first fraction by n%2Fn to get the denominator equal to the LCD


Multiply the second fraction by %28n%2B2%29%2F%28n%2B2%29 to get the denominator equal to the LCD


Distribute


%282n%2Bn%2B2%2Bn%2B6%29%2F%28n%28n%2B2%29%29 Combine the fractions


%284n%2B8%29%2F%28n%28n%2B2%29%29 Combine like terms.


%284%28n%2B2%29%29%2F%28n%28n%2B2%29%29 Factor out the GCF


%284%2Across%28%28n%2B2%29%29%29%2F%28n%2Across%28%28n%2B2%29%29%29 Cancel out like terms


4%2Fn Simplify


So 2%2F%28n%2B2%29+%2B+1%2Fn+%2B+%28n%2B6%29%2F%28n%5E2%2B2n%29=4%2Fn where n%3C%3E-2 or n%3C%3E0