回答:
答えは #=2#
説明:
#x = a /(b + c)#
#y = b /(c + a)#
#z = c /(a + b)#
したがって、
#1 /(1 + x)= 1 /(1 + a /(b + c))=(b + c)/(a + b + c)#
#1 /(1 + y)= 1 /(1 + b /(c + a))=(c + a)/(a + b + c)#
#1 /(1 + z)= 1 /(1 + c /(a + b))=(a + b)/(a + b + c)#
最後に、
#1 /(1 + x)+ 1 /(1 + y)+ 1 /(1 + z)#
#=(b + c)/(a + b + c)+(c + a)/(a + b + c)+(a + b)/(a + b + c)#
#=(b + c + c + a + a + b)/(a + b + c)#
#=(2(a + b + c))/(a + b + c)#
#=2#