Question

Решите уравнения:

$frac{7}{x-2} = frac{5}{x+3}$


$frac{x}{x-1} = frac{4}{x}$


$frac{x-1}{x+3}= frac{x+3}{x+1}$

Answer 1

$frac{7}{x-2} = frac{5}{x+3} \ 7x+21=5x-10 \ 2x=-31 \ x=-15.5$

$frac{x}{x-1} = frac{4}{x} \ x^2=4x-4 \ x^2-4x+4=0 \ (x-2)^2=0 \ x-2=0 \ x=2$

$frac{x-1}{x+3}= frac{x+3}{x+1} \ (x-1)(x+1)=(x+3)^2 \ x^2-1=x^2+6x+9 \ 6x+10=0 \ x=- frac{10}{6} =- frac{5}{3}$

Answer 2

7/(x-2) = 5/(x+3)
x не равно 2 и -3
7(x+3)=5(x-2)
7x+21=5x-10
2x=-31
x=-31/2


x/(x-1)=4/x
x не равно 0 1
x2=4x-4
x2-4x+4
(x-2)2=0
x=2

(x-1)/(x+3)=(x+3)/(x+1)
x не равно -1 -3
(x+1)(x-1)=(x+3)(x+3)
x2-1=x2+6x+9
6x=-10
x=-5/3