Question

If x=(a-b)/(a+b), y=(b-c)/(b+c), z=(c-a)/(c+a), find {(1+x)(1+y)(1+z)}/{(1-x)(1-y)(1-z)}

Answer 1

Given,

x=(a-b)/(a+b), y =(b-c)/(b+c), z=(c-a)/(c+a) ----(1)

=> 1+x =(1+a-b)/(a+b)

=>1+y=(1+b-c)/(b+c)

=>1+z=(1+c-a)/(c+a)

=>1+x =(a+b+a-b)/(a+b)

=>1+y=(b+c+b-c)/(b+c)

=>1+z=(c+a+c-a)/(c+a)

=>1+x =2a/(a+b), 1+y=2b/(b+c), 1+z=2c/(c+a)---(2)

From equation (1),

=>1-x =(1-a-b)/(a+b)

=>1-y=(1-b-c)/(b+c)

=>1-z=(1-c-a)/(c+a)

=>1-x =(a+b-a+b)/(a+b)

=>1-y=(b+c-b+c)/(b+c)

=>1-z=(c+a-c+a)/(c+a)

=>1-x =2b/(a+b), 1-y=2c/(b+c), 1-z=2a/(c+a) ---(3)

From equation (2) and (3),

=>(1+x)/(1-x)=a/b

=>(1+y)/(1-y)=b/c

=>(1+z)/(1-z)=c/a

=>{(1+x)(1+y)(1+z)}/{(1-x)(1-y)(1-z)}=abc/abc=1

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Answer 2

Answer:

Refer to the attachment for solution......