SOLUTION: Need help adding and subtracting (a-1)/(a+1)+(a+1)/(a-1) do they cancel each other out? and (b)/(b-1)+(2b)/(b^2-1)????? Thank you in advance!

Question 288175: Need help adding and subtracting (a-1)/(a+1)+(a+1)/(a-1) do they cancel each other out? and (b)/(b-1)+(2b)/(b^2-1)????? Thank you in advance!
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
NO they do not cancel.
(a-1)/(a+1)+(a+1)/(a-1) Find a common denominator & add.
[(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.
---------------------------
(b)/(b-1)+(2b)/(b^2-1)
[b(b^2-1)+2b(b-1)]/(b-1)(b^2-1)
b^3-b+2b^3-2b]/(b-1)(b^2-1)
(3b^3-3b)/(b-1)(b^2-1)
3b(b^2-1)/(b-1)(b^2-1) cancel out the (b^2-1) terms.
3b/(b-1) ans.
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