1
1)(x+y)/(x-y)-(x-y)/(x+y)=(x²+2xy+y²-x²+2xy+y²)/([(x-y)(x+y)]=4xy/(x²-y²)
2)(x²+y²)/(x²-y²)+(x²-y²)/(x²+y²)=(x^4+2x²y²+y^4-x^4+2x²y²-y^4)/[(x²-y²)(x²+y²)]
=4x²y²/[(x²-y²)(x²+y²)]
3)4xy/(x²-y²)*(x²-y²)(x²+y²)/4x²y²=(x²+y²)/xy
2
(a^6-b^6)/(a²-b²)-(a^6+b^6)/(a²+b²)=
=(a^8+a^6b²-a²b^69-b^8-a^8-a²b^6+a^6b²+b^8)/(a^4-b^4)=
=(2a^6b²-2a²b^6)/(a^4-b^4)=2a²b²(a^4-b^4)/(a^4-b^4)=2a²b²