यदि `(x+1)/(x-1)=a/b` और `(1-y)/(1+y)=b/a`, तो `(x-y)/(1+xy)` का मान क्या होगा?

Options

A. `(a^(2)-b^(2))/(ab)`
B. `(a^(2)+b^(2))/(2ab)`
C. `(a^(2)-b^(2))/(2ab)`
D. `(2ab)/(a^(2)-b^(2))`

Answer

D

Explanation

Given:
`implies(x+1)/(x-1)=a/b`
`implies x/1=(a+b)/(a-b)`
(using componento & dividendo)
`implies x=(a+b)/(a-b)`…………i
Again,
`implies (1-y)/(1+y)=b/a`
`implies (1+y)/(1-y)=a/b`
`implies 1/y=(a+b)/(a-b)`
`implies y=(a-b)/(a+b)`…………i
`implies` Fro question `(x-y)/(1+xy)`
`implies (((a+b)/(a-b)-((a-b))/(a+b)))/(1+((a+b)/(a-b))((a-b)/(a+b)))`
`implies ((a+b)^(2)-(a-b)^(2))/((a^(2)-b^(2))(1+1))`
`implies (4ab)/(2(a^(2)-b^(2)))implies(2ab)/(a^(2)-b^(2))`