SOLUTION: Can someone help me and tell me where I am going wrong in this problem? 3c+d / Cd^2 + c-d / c^2d I have the LCD to be c^2d^2 and added it up to be (3c+d)(c-d) / c^2d^2 but my

Question 708316: Can someone help me and tell me where I am going wrong in this problem?
3c+d / Cd^2 + c-d / c^2d
I have the LCD to be c^2d^2
and added it up to be (3c+d)(c-d) / c^2d^2
but my book says the answer should be (3c-d)(c+d) / c^2d^2

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
(3c+d)/(cd^2) + (c-d)/(c^2d)
indeed, the LCD is c^2d^2:
(3c+d)/(cd^2)*c/c + (c-d)/(c^2d)*d/d
c(3c+d)/(c^2d^2) + d(c-d)/(c^2d^2)
(3c^2+cd)/(c^2d^2) + (cd-d^2)/(c^2d^2)
(3c^2+cd + cd-d^2)/(c^2d^2)
(3c^2+2cd-d^2)/(c^2d^2)
Notice:3c^2+2cd-d^2 factors as (3c-d)(c+d) (I think this is where you went wrong)
resulting in
(3c-d)(c+d)/(c^2d^2)

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