(((b+c+a)/(b+c-a))*((1+(b^2+c^2-a^2)/(2*b*c))))
It's been a minute since I have done much with algebra, but if you are looking to simplify I believe this is correct.
First part cancels out so (b+c+a) / (b+c+a) = 1
Then you can remove the squares by dividing like variables.
(1 + (b^2 + c^2 - a^2)) / (2*b*c) =
(1 + b + c - a^2) / (2)
Combining the first parts we have
1 * (1 + b + c - a^2) / (2) =
Multiplying by one, we can just drop the one.
(1 + b + c - a^2) / (2) =
dividing by 2 we have
0.5 + 0.5b + 0.5c - 0.5a^2 =
Then we can simplify further
0.5 + 0.5(b+c-a^2)