Question

Tinh:

\(\dfrac{2xy}{x^2-y^2}+\dfrac{x-y}{2x+2y}+\dfrac{y}{y-x}\)

Answer 1

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

=2xy.2/2(x+y)(x-y) + (x-y)^2/2(x+y)(x-y) + -y.2(x+y)/2(x+y)(x-y)

=4xy/2(x+y)(x-y) + x^2-2xy+y^2/2(x+y)(x-y) + -2xy-2y^2/2(x+y)(x-y)

=4xy+x^2-2xy+y^2-2xy-2y^2/2(x+y)(x-y)

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