Question

( x /x+y + y/x-y ) ÷
(x /x-y - y/x+y )=_______?​

Answer 1

Step-by-step explanation:

Given :-

(x /x+y + y/x-y ) ÷(x /x-y - y/x+y )

To find :-

Simplify the expression?

Solution :-

Given expression is

(x /x+y + y/x-y ) ÷(x /x-y - y/x+y )

=> [x(x-y)+y(x+y)]/[(x+y)(x-y)] ÷

[x(x+y)-y(x-y)]/[(x+y)(x-y)]

On cancelling (x+y)(x-y) then

=> [x(x-y)+y(x+y)]/[x(x+y)-y(x-y)]

=> (x²-xy+xy+y²) ÷ (x²+xy-xy+y²)

=> (x²+y²)÷(x²+y²)

=> (x²+y²)/(x²+y²)

=> 1

Answer :-

The value of (x /x+y + y/x-y ) ÷(x /x-y - y/x+y ) is 1