X is the reciprocal of y then x+y÷x-y is equal to
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if x is reciprocal of y then x=1/y
so the given expression becomes
(1/y + y) ÷ (1/y - y)
= ( 1+ y^2)/y ÷ ( 1- y^2)/y
= ( 1+ y^2)/y × y/( 1- y^2)
=( 1+ y^2)/(1- y^2)
so the given expression becomes
(1/y + y) ÷ (1/y - y)
= ( 1+ y^2)/y ÷ ( 1- y^2)/y
= ( 1+ y^2)/y × y/( 1- y^2)
=( 1+ y^2)/(1- y^2)
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