(2xy/x^2-y^2 x-y/2x 2y) - 2x/x y y/y-x = 1

Lời giải:

\(A = \left( {\frac{{2{\rm{x}}y}}{{{x^2} - {y^2}}} + \frac{{x - y}}{{2{\rm{x}} + 2y}}} \right):\frac{{x + y}}{{2{\rm{x}}}} + \frac{y}{{y - x}}\)\( = \left( {\frac{{4{\rm{x}}y}}{{2(x - y)(x + y)}} + \frac{{{{(x - y)}^2}}}{{2(x + y)(x - y)}}} \right):\frac{{x + y}}{{2{\rm{x}}}} + \frac{y}{{y - x}}\) 

\( = \frac{{4{\rm{x}}y + {x^2} - 2{\rm{x}}y + {y^2}}}{{2(x - y)(x + y)}}.\frac{{2{\rm{x}}}}{{x + y}} + \frac{y}{{y - x}}\)

\( = \frac{{{x^2} + 2{\rm{x}}y + {y^2}}}{{2(x - y)(x + y)}}.\frac{{2{\rm{x}}}}{{x + y}} + \frac{y}{{y - x}}\).

\( = \frac{{2{\rm{x}}{{(x + y)}^2}}}{{2(x - y){{(x + y)}^2}}} + \frac{y}{{y - x}} = \frac{x}{{x - y}} + \frac{y}{{y - x}} = \frac{{x - y}}{{x - y}} = 1\).