SOLUTION: {{{(a-1)/(a+1) + (a+1)/(a-1)}}} I need to add the fractions together!

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Question 271684: %28a-1%29%2F%28a%2B1%29+%2B+%28a%2B1%29%2F%28a-1%29 I need to add the fractions together!
Found 3 solutions by checkley77, richwmiller, Edwin McCravy:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(a-1)/(a+1)+(a+1)/(a-1)
[(a-1)(a-1)+(a+1)(a+1)]/(a+1)(a-1)
[a^2-2a+1+a^2+2a+1]/(a^2-1)
[2a^2+2)/(a^2-1)
2(a^2+1)/(a^2-1) ans.

Answer by richwmiller(17219) About Me  (Show Source):
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
%28a-1%29%2Fred%28a%2B1%29+%2B+%28a%2B1%29%2Fgreen%28a-1%29 I need to add the fractions together! 

Put parentheses around all the numerators and denominators:

%28%28a-1%29%29%2Fred%28%28a%2B1%29%29+%2B+%28%28a%2B1%29%29%2Fgreen%28%28a-1%29%29

The LCD is red%28%28a%2B1%29%29green%28%28a-1%29%29

The first fraction's denominator needs an green%28%28a-1%29%29 to become
the LCD, so we multiply it by green%28%28a-1%29%29%2Fgreen%28%28a-1%29%29 which 
equals 1 and thus will not change the value.




The second fraction's denominator needs an red%28%28a%2B1%29%29 to become
the LCD, so we multiply it by red%28%28a%2B1%29%29%2Fred%28%28a%2B1%29%29 which 
equals 1 and thus will not change the value.




Now the denominators are the same in value so we can
combinew the numerators over the LCD:



Multiply the numerator out but not the denominator.


%28%28a%5E2-2a%2B1%29+%2B+%0D%0A%0D%0A%28a%5E2%2B2a%2B1%29%29%2F%28%28a-1%29%28a%2B1%29%29

%28a%5E2-2a%2B1+%2B+%0D%0A%0D%0Aa%5E2%2B2a%2B1%29%2F%28%28a-1%29%28a%2B1%29%29



%282a%5E2+%2B2%29%2F%28%28a-1%29%28a%2B1%29%29

%282%28a%5E2+%2B1%29%29%2F%28%28a-1%29%28a%2B1%29%29

Since nothing will factor or cancel further,
we may multiply the numerator and demominate back out:

%282a%5E2+%2B2%29%2F%28a%5E2-1%29

Edwin