Объяснение:
(x+1)/(x-4) = (3x+1)/(3x-1)
ОДЗ : х не = 4 и х не = 1/3
(x+1)(3x-1) = (3x+1)(x-4)
3x^2 -x+3x-1 = 3x^2 -12x+x-4
13x = -3
х = -3/13
2). (9x-7)/(3x-2) - (4x-5)/(2x-3) = 1
ОДЗ : х не = 2/3 и х не = 3/2
(9x-7)(2x-3) - (4x-5)(3x-2) = (3x-2)(2x-3)
18x^2 -27x-14x+21-12x^2 +8x+15x-10 = 6x^2 -9x-4x+6
5x = 5
х = 1
3). (x^2 +20)/(x^2 -4) = (x-3)/(x+2) - 6/(2-x)
(x^2 +20)/(x+2)(x-2) = (x-3)/(x+2) + 6/(x-2)
ОДЗ : х не = 2 и х не = -2
x^2 +20 = (x-3)(x-2) + 6(x+2)
x^2 +20 = x^2 -2x-3x+6+6x+12
х = 2 (не подходит по ОДЗ)
Нет решения.
4). 5/(x^2 -7x) - (x-5)/(x^2 +7x) - 9/(x^2 -49) = 0
5/x(x-7) - (x-5)/x(x+7) - 9/(x+7)(x-7) = 0
ОДЗ : х не = 0, х не = 7 и х не = -7
5(x+7) - (x-5)(x-7) - 9x = 0
5x+35-x^2 +7x+5x-35-9x = 0
x^2 - 8x = 0
x(x-8) = 0
x1 = 0 (не подходит по ОДЗ)
= х² - 2*х *1 + 1² + (2х)² + 2*2х * 1 + 1² =
= х² - 2х + 1 + 4х² + 4х + 1=
= (х² +4х²) + (4х - 2х) + 2 =
= 5х² + 2х + 2
(3-4у)(4у+3) = (3-4у)(3+4у) = 3² - (4у)² = 9 - 16у²
(3-а)(9 +3а+а²) = (3-а)(3² +3а +а²) = 3³ -а³ = 27 - а³
(2а+1)³ = (2а)³ + 3*(2а)² *1 + 3 *2а * 1² + 1³ =
= 8а³ + 12а² +6а + 1