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If a=x/(x+y) and b=y/(x-y) , then (a b)/...

If `a=x/(x+y)` and `b=y/(x-y)` , then `(a b)/(a+b)` is equal to `(x y)/(x^2+y^2)` (b) `(x^2+y^2)/(x y)` (c) `x/(x+y)` (d) `(y/(x+y))^2`

A

` ( xy)/( x^(2) + y^(2)) `

B

` ( x^(2) + y^(2))/(xy)`

C

`(x)/( x + y) `

D

` (( x)/( x + y))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(ab)/(a + b) + (( x)/(( x + y)) xx ( y)/(( x - y)))/( ( x)/( ( x + y)) + (y)/( ( x - y))) `
` = (( xy)/((x + y) ( x - y)))/(( x ( x - y) + y ( x + y))/(( x + y) ( x - y)))`
` = (xy)/( x^(2) - xy + xy + y^(2)) =( xy)/(x^(2) + y^(2))`
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