Question

Решите по действиям 9 пример, пожалуйста. Заранее благодарю)

Answer 1

1)(x+y)/(x-y)+(x-y)/(x+y)=[(x+y)²+(x-y)²]/(x²-y²)=(x²+2xy+y²+x²-2xy+y²)/(x²-y²)=
=2(x²+y²)/(x²-y²)
2)(x+y)/(x-y)-(x-y)/(x+y)=[(x+y)²-(x-y)²]/(x²-y²)=(x+y-x+y)(x+y+x-y)/(x²-y²)=
=2y*2x/(x²-y²)=4xy/(x²-y²)
3)2(x²+y²)/(x²-y²) :4xy/(x²-y²)=2(x²+y²)/(x²-y²) * (x²-y²)/4xy=(x²+y²)/2xy
4)(x²+y²)/2xy*x²y²/[(x-y)²+(x+y)²]=(x²+y²)/2xy*x²y²/(x²-2xy+y²+x²+2xy+y²)=
=(x²+y²²)/2xy*x²y²/[2(x²+y²)]=xy/4