№ 1.
(Y²-36)/у =0
Y²-36=0; у≠0
Y²=36
у1 = 6; у2= -6
Ответ. у1 = 6; у2= -6
№ 2
(5t+2)/6 =(2t-1)/8
8(5t+2) - 6(2t-1) = 0
40t + 16 - 12t + 6 = 0
28t + 22 = 0
28t = -22
t = - 11/14
Ответ. t = - 11/14
№ 4
(25-y²)/5y = 0
25-y² =0 ; у≠0
y²=25
у1 = -5, у2 = 5
Ответ. у1 = -5, у2 = 5
№ 5
(3x-5)/(x²+2) = 3/x
(3x-5)/(x²+2) - 3/x = 0
(х*(3x-5) - 3*(x²+2))/(x*(x²+2)) = 0
х*(3x-5) - 3*(x²+2) = 0 и x*(x²+2) ≠ 0: x≠0, x≠-√2, x≠√2
3х²-5х-3х²-6 = 0
-5х-6=0
5х = -6
х = -6/5 = -1,2
Ответ. х = -1,2
№ 6
3/t + 27/(t²-9t) = (t-2)/(t-9)
t + 27/t(t-9) - (t-2)/(t-9) = 0
(3(t-9) + 27 - t(t-2))/(t(t-9)) = 0
3(t-9) + 27 - t(t-2) = 0 и t(t-9) ≠ 0 t≠0, t≠9
3t - 27 + 27 - t² +2t = 0
5t - t²=0
t(5-t)=0
t=0 (не удовл) t = 5
Ответ. t = 5