Question

If x=a-b/a+b,y=b-c/b+c,z=c-a/c+a,then the value of (1+x)(1+y)(1+z)/(1-x)(1-y)(1-z) is

Answer 1

Answer:

x=a-b/a+b

y=b-c/b+c

z=c-a/c+a

now,

(1+x)(1+y)(1+z)/(1-x)(1-y)(1-z)

=(1+a-b/a+b)(1+b-c/b+c)(1+c-a/c+a)/{1-(a-b/a+b)} {1-(b-c/b+c)} {1-(c-a)(c+a)}

=(a+b+a-b/a+b)(b+c+b-c/b+c)(c+a+c-a/c+a)(a+b-a+b/a+b)(b+c-b+c/b+c)(c+a-c+a/c+a)

={(2a/a+b)(2b/b+c)(2c/c+a)}/{(2b/a+b)(2c/b+c)(2a/c+a)}

=1