Verified answer

№ 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