А) (у-4/3у-3 + 1/у-1) : у+1/3 + 2/у²-1 = 1/у-1
1) у-4/3у-3 + 1/у-1 = у-4/(у-1) + 1/у-1 = у-4+3/3(у-1) = у-1/3(у-1) = 1/3
2) 1/3 * 3/у+1 = 1/у+1
2) 1/у+1 + 2/у²-1 = 12/у+1 + 2/(у+1)(у-1) = у-1+2/(у+1)(у-1) = 1/у-1
б) b/a-b * (1/a - 1/b) = -1/a
1) 1/a - 1/b = b-a/ab
2) b/a-b * b-a/ab = -b(a-b)/(a-b)ab = -1/a
в) a³+ba²/a-b * a²-b²/a²+2ab+b² * (1/a+ 1/b) = a²+ab/b
1) 1/a + 1/ = a+b/ab
2) a³+ba²/a-b * a²-b²/a²+2ab+b² = a²(a+b)(a-b)(a+b)/(a-b)(a+b)² = a²
3) a² * a+b/ab = a(a+b)/b = a²+ab/b
г) (х+у)²/(х+у)²-(х-у)² : (х/у - у/х) = х+у/4х-4у
1) х/у - у/х = х²-у²/ху=(х+у)(х-у)/ху
2) (х+у)²/(х+у)²-(х-у)² : (х+у)(х-у)/ху = (х+у)²/(х+у)²-(х-у)² * ху/(х+у)(х-у) = (х+у)² * ху/(х+у+х-у)(х+у-х+у) * (х-у)(х+у) = (х+у)² * ху/2х*2у(х-у)(х+у) = (х+у)² * ху/4ху(х-у)(х+у) =х+у/4(х-у) = х+у/4х-4у