Y + 3/(у - 1) = (2у + 3)/(у - 1)
y + 3/(у - 1) - (2у + 3)/(у - 1) = 0
y(y - 1)/(y - 1) + 3/(у - 1) - (2у + 3)/(у - 1) = 0
(y(y - 1) + 3 - (2y + 3))/(y - 1) = 0
(y² - 1 + 3 - 2y - 3)/(y - 1) = 0
(y² - 2y - 1 + 0)/(y - 1) = 0
y(y - 2 - 1)/(y - 1) = 0
y(y - 3)/(y - 1) = 0
y/(y - 1) = 0 | · (y - 1)
y₁ = 0
(y - 3)/(y - 1) = 0 | · (y - 1)
y - 3 = 0
y₂ = 3
Ответ: y₁ = 0; y₂ = 3
(2у - 8)/(у - 5) + 10/(у ²- 25) = (у + 4)/(у + 5)
(2у - 8)/(у - 5) + 10/(у² - 25) - (у + 4)/(у + 5) = 0
2(y - 4)/(y - 5) + 10/(y - 5)(y + 5) - (у + 4)/(у + 5) = 0
2(y - 4)(y + 5)/(y - 5)(y + 5) + 10/(y - 5)(y + 5) - (y - 5)(y + 4)/(y + 5)(y - 5) = 0
(2(y- 4)(y + 5) + 10 - (y - 5)(y + 4))/(y + 5)(y - 5) = 0
(2(y² - 4y + 5y - 20) + 10 - (y² - 5y + 4y - 20))/(y + 5)(y - 5) = 0
(2y² - 8y + 10y - 40 + 10 - y² + 5y - 4y + 20)/(y + 5)(y - 5) = 0
(y² + 3y - 10)/(y + 5)(y - 5) = 0 | · (y + 5)(y - 5)
y² + 3y - 10 = 0
a = 1; b = 3; c = (-10)
D = b² - 4ac = 3² - 4 · 1 · (-10) = 9 - 4 · (-10) = 9 + 14 = 13
y₁ = ((-b) + √D)/2a = ((-3) + √13)/2 · 1 = ((-3) + 3,60555)/2 = (-10,81665)/2 =
= (-5,4833)
y₂ = ((-b) - √D)/2a = ((-3) - √13)/2 · 1 = ((-3) - 3,60555)/2 = (-6,60555)/2 =
= (-3,302775)