Question 1005149
Multiply both sides by (a+c)(b+c)(a+b+c) to clear out the fractions and make life easier. That is, statement holds if and only if


*[tex \large (b+c)(a+b+c) + (a+c)(a+b+c) = 3(a+c)(b+c)]


With some simplification, this is equivalent to


*[tex \large a^2 + b^2 = c^2 + ab]


or


*[tex \large c^2 = a^2 + b^2 - ab]


However this statement is true by applying the law of cosines on triangle ABC, as angle C = 60 degrees.