Question

2x+3/x+2=3x+2/x решите по братски

Answer 1

(2x+3) / (x+2) = (3x+2) / x,

х(2x+3) / х(x+2) = (х+2)(3x+2) / x(х+2),

(2x²+3х) / х(x+2) = (3х²+2х+6х+4) / x(х+2),

(2x²+3х - 3х²-2х-6х-4) / x(х+2) = 0,

(-х²-5х-4) / x(х+2) = 0,

ОДЗ:

x(х+2) ≠ 0,

х ≠ 0,    х+2 ≠ 0,

            х ≠ -2,

-х²-5х-4 = 0,

х² + 5х + 4 = 0,

Д = 5² - 4*1*4 = 25 - 16 = 9,

х1 = (-5 + 3) / 2*2 = -2/2 = -1,

х2 = (-5 - 3) / 2*1 = -8/2 = -4