Step-by-step explanation:
y²-x²= (y+x)(y-x) = (x+y)(y-x) = -(x+y)(x-y)
So, expression becomes
[tex] \frac{x}{x-y} + \frac{y}{x+y} + \frac{-2xy}{(x+y)(x-y)} [/tex]
Taking LCM (x+y)(x-y)
[tex] = \frac{x(x + y) + y(x - y) - 2xy}{(x + y)(x - y)} [/tex]
[tex] = \frac{ {x}^{2} + xy + xy - {y}^{2} - 2xy }{(x + y)(x - y)} [/tex]
[tex] = \frac{ {x}^{2} + {y}^{2} + 2xy - 2xy}{(x + y)(x - y)} [/tex]
[tex] = \frac{ {x}^{2} - {y}^{2} }{(x + y)(x - y)} [/tex]
[tex] = \frac{(x + y)(x - y)}{(x + y)(x - y)} [/tex]
= 1
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Verified answer
Step-by-step explanation:
y²-x²= (y+x)(y-x) = (x+y)(y-x) = -(x+y)(x-y)
So, expression becomes
[tex] \frac{x}{x-y} + \frac{y}{x+y} + \frac{-2xy}{(x+y)(x-y)} [/tex]
Taking LCM (x+y)(x-y)
[tex] = \frac{x(x + y) + y(x - y) - 2xy}{(x + y)(x - y)} [/tex]
[tex] = \frac{ {x}^{2} + xy + xy - {y}^{2} - 2xy }{(x + y)(x - y)} [/tex]
[tex] = \frac{ {x}^{2} + {y}^{2} + 2xy - 2xy}{(x + y)(x - y)} [/tex]
[tex] = \frac{ {x}^{2} - {y}^{2} }{(x + y)(x - y)} [/tex]
[tex] = \frac{(x + y)(x - y)}{(x + y)(x - y)} [/tex]
= 1
Mark as brainliest