2х / (х² - у²) : ( 1/(х²+2ху +у²) + 1/(у² - х²) ) =
= 2х/(х²-у²) : ( 1/(х+у)² + 1/(у-х)(у+х) ) =
= 2х/(х²-у²) : ( (у-х + x+y) / (у-х)(х+у)² ) =
= [ 2х/(х-у)(х+у) ] × [ (у-х)(х+у)² / 2y ] =
= (2x ×(y-x)(x+y)² ) / (-1(y-x)(x+y)×2y) =
= x(x+y) / ( - 1 * y) =
= - x(x+y)/y
можно еще раскрыть скобки
= - (х²+ху)/у = - (х²/у + х)
((2а - 3)/(а²-4а +4) - (а-1)/(а²-2а) ) : (а²-2)/(а³ - 4а) =
= ((2а-3)/(а - 2)² - (а-1)/а(а-2) ) : (а²-2)/а(а² -4) =
= [ ( (2а-3)*а - (а-1)*(а-2) ) / ( а(а-2)² ) ] × [ (a(a-2)(a+2)) / (a² -2) ] =
= [ (2a²-3a - (a²-2a-a+2) ) / (a(a-2)² ) ] × [(a(a-2)(a+2) ) / (a² - 2)]=
= [ (2a² - 3a -a² +3a - 2) / (a(a-2)² ) ] × [ (a(a-2)(a+2) ) / (a² - 2) ] =
= [(a² -2) / a(a-2)² ] × [ a(a-2)(a+2) / (a² - 2) ]=
= (a+2)/(a-2)