SOLUTION: Add these expressions. a+6/a+2 + 16/a^2-4

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Question 17594: Add these expressions.
a+6/a+2 + 16/a^2-4
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean +%28a%2B6%29%2F%28a%2B2%29+%2B+16%2F%28a%5E2-4%29+?? If so, then the first step in adding fractions is to factor the denominators so as to find the LCD.

+%28a%2B6%29%2F%28a%2B2%29+%2B+16%2F%28%28a-2%29%28a%2B2%29%29+ and the LCD = (a-2)(a+2).

In order to get the LCD in the first fraction, you already have the (a+2) factor, but you will need to multiply numerator and denominator of this first fraction by (a-2). The second fraction already has the LCD, so leave it alone.



Now you have an LCD of (a-2)(a+2), and this becomes THE denominator of the fraction:
+%28______________________%29%2F%28%28a-2%29%2A%28a%2B2%29%29+

Now, just add numerators together as follows:
+%28+a%5E2+%2B4a-12+%2B+16%29%2F%28%28a-2%29%2A%28a%2B2%29%29+

Simplify: %28a%5E2+%2B+4a+%2B4%29%2F%28%28a-2%29%28a%2B2%29%29

The numerator DOES factor, so you must factor the numerator in order to reduce the fraction.
%28%28a%2B2%29%2A%28a%2B2%29%29%2F%28%28a-2%29%28a%2B2%29%29

Divide out the (a+2) factor in the denominator with one of the numerator factors:
+%28a%2B2%29%2F%28a-2%29+ FINAL ANSWER!!

R^2 at SCC