Question

x+1 2x-1
---- = --------
x-1 3x+1

Answer 1

$frac{x + 1}{x - 1} = frac{2x - 1}{3x + 1}$ (х≠1 и -1/3)

Используем основное свойство пропорции

($frac{a}{b} = frac{c}{d} < = > ad = bc$) получим

$(x + 1)(3x + 1) = (x - 1)(2x - 1) \ 3x {}^{2} + x + 3x + 1 = 2x {}^{2 } - x - 2x + 1 \ 3x {}^{2} +4x + 1 = 2x {}^{2 } -3x + 1 \ x {}^{2} + 7x = 0 \ x(x + 7) = 0 \ x1 = 0 \ x2 = - 7$

Ответ: х1=0, х2=-7

Answer 2

(x+1)×(3x+1)=(2x-1)×(x-1)
x-1≠0
x≠1
3x+1≠0
3x=-1|÷3
x≠(-1/3)
3x²+x+3x+1=2x²-2x-x+1
3x²+4x+1=2x²-3x+1
3x²+4x+1-2x²+3x-1=0
x²+7x=0
x(x+7)=0

x1=0

x2+7=0

x2=-7

Проверка:

(х+1)/(х-1)=(2х-1)/(3х+1)

х1=0
(0+1)/(0-1)=(2×0-1)/(3×0+1)
1/(-1)=(-1)/1
-1=-1- истина.

х2=-7
(-7+1)/(-7-1)=(2×(-7)-1)/(3×(-7)+1)
(-6)/(-8)=(-15)/(-20)
(3/4)=(3/4)- истина.

Ответ: х1=0 и х2=-7