Question

find the value with complete steps

Answer 1

pqr = 1
now ,

1/( 1+ p + r-1) = 1/( 1+ p + 1/r)

= r/( r + pr + 1)

= r/( r + 1/q + 1) { from pqr = 1 , pr = 1/q

= rq/( rq + 1 + q)

=p-1/( p-1 + 1 + q) ----------(1)

similarly ,
1/( 1+ q + r-1) = r/( r + qr + 1 )

= r/( r+ 1/p + 1) { from pqr = 1 , qr = 1/p }

= r/( r+ p-1 + 1) ----------------(2)

now put equations (1) and (2) in above ,

p-1/( p-1 + q +1 ) + r/( r + p-1 +1) +1/( 1 + r + p-1)

= ( p-1 + r + 1)/( p-1 + r +1)

= 1 ( answer )

Answer 2

Answer:

pqr = 1

now ,

1/( 1+ p + r-1) = 1/( 1+ p + 1/r)

= r/( r + pr + 1)

= r/( r + 1/q + 1) { from pqr = 1 , pr = 1/q

= rq/( rq + 1 + q)

=p-1/( p-1 + 1 + q) ----------(1)

similarly ,

1/( 1+ q + r-1) = r/( r + qr + 1 )

= r/( r+ 1/p + 1) { from pqr = 1 , qr = 1/p }

= r/( r+ p-1 + 1) ----------------(2)

now put equations (1) and (2) in above ,

p-1/( p-1 + q +1 ) + r/( r + p-1 +1) +1/( 1 + r + p-1)

= ( p-1 + r + 1)/( p-1 + r +1)

= 1 ( answer )