# Math Help - prove the identity

1. ## prove the identity

if x = (2ab+2bc+2ca)/(a+b+c), then prove that,

[(x+a)/(x-a)] + [(x+b)/(x-b)] +[(x+c)/(x-c)] - [6abc/(x-a)(x-b)(x-c)] = 3

2. Originally Posted by earthboy
if x = (2ab+2bc+2ca)/(a+b+c), then prove that,

[(x+a)/(x-a)] + [(x+b)/(x-b)] +[(x+c)/(x-c)] - [6abc/(x-a)(x-b)(x-c)] = 3
is that menth to be $\frac{6abc}{(x-a)(x-b)(x-c)}$
or as it is written $\frac{6abc}{x-a}\times(x-b)(x-c)$

3. Quote:
Originally Posted by earthboy
if x = (2ab+2bc+2ca)/(a+b+c), then prove that,

[(x+a)/(x-a)] + [(x+b)/(x-b)] +[(x+c)/(x-c)] - [6abc/(x-a)(x-b)(x-c)] = 3
start by combining the first three terms on the left with the last term using the common denominator $(x-a)(x-b)(x-c)$