Решение
1) (t² - 5t)/(t + 5) = 0
t² - 5t = 0
t + 5 ≠ 0, t ≠ - 5
t² - 5t = 0
t(t - 5) = 0
t1 = 0
t - 5 = 0
t2 = 5
Ответ: t1 = 0 ; t2 = 5
2) (4a - 5)/(a² + 1 = 4/a
(4a - 5)*a = 4*(a² + 1)
4a² - 5a = 4a² + 4
- 5a = 4
a = - 0,8
Ответ: a = - 0,8
3) 35/(x² + 7x) - 5/x = (x + 3)/(x + 7)
35/(x² + 7x) - 5/x - (x + 3)/(x + 7) = 0
(35 - 5x - 35 - x² - 3x)/(x² + 7x) = 0
- x² - 8x = 0
x(x + 7) ≠ 0, x≠ 0, x≠ - 7
- x² - 8x = 0
- x( x + 8) = 0
x1 = 0
x + 8 = 0,
x2 = - 8
Ответ: х2 = - 8