SOLUTION: I really would like some help on the rational addition expression...Thank you for all your help!! n - 2 n^2 + 5n + 10 ----- + ----------- -- n + 4 n

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Question 136138: I really would like some help on the rational addition expression...Thank you for all your help!!

n - 2 n^2 + 5n + 10
----- + --------------
n + 4 n + 4
Found 2 solutions by solver91311, vleith:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28n-2%29%2F%28n%2B4%29%29%2B%28%28n%5E2%2B5n%2B10%29%2F%28n%2B4%29%29

Notice that the denominators are equal. Therefore you can simply add the numerators directly without having to discover and apply a lowest common denominator.

%28%28n-2%29%2B%28n%5E2%2B5n%2B10%29%29%2F%28n%2B4%29

%28n%5E2%2B6n%2B8%29%2F%28n%2B4%29

Since 2%2A4=8 and 2%2B4=6, the numerator trinomial factors to:

%28n%2B2%29%28n%2B4%29, so the rational expression reduces to:

%28%28n%2B2%29%28n%2B4%29%29%2F%28n%2B4%29.

But %28n%2B4%29%2F%28n%2B4%29=1, so eliminate these factors from numerator and denominator leaving you with:

n%2B2

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given: %28%28n-2%29%2F%28n%2B4%29%29+%2B+%28%28n%5E2+%2B+5n+%2B+10%29%2F%28n%2B4%29%29+
Before one can add fractions, they must have a common denominator. In this problem, each fraction has a denominator of %28n%2B4%29. So, the two fractions can be added in their current form
%28%28n-2%29%2F%28n%2B4%29%29+%2B+%28%28n%5E2+%2B+5n+%2B+10%29%2F%28n%2B4%29%29+
%28%28n-2%29+%2B+%28n%5E2+%2B+5n+%2B+10%29%29%2F%28n%2B4%29
Now you can collect like terms
%28n%5E2+%2B+5n+%2B+n+%2B+10+-2%29%2F%28n%2B4%29
%28n%5E2+%2B+6n+%2B+8%29%2F%28n%2B4%29
factor the numerator
%28%28n%2B4%29%28n%2B2%29%29%2F%28n%2B4%29+
n%2B2 where n!= -4