решите уравнение 1/х+3+3/х-1=х^2+5х+2/х^2+2x-3. Created by 1234554321c. algebra-ru

х^2+2x-3...

August 2022 2 9 Report

решите уравнение
1/х+3+3/х-1=х^2+5х+2/х^2+2x-3

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1/(x+3)+3/(x-1)=(x²+5x+2)/(x+3)(x-1)
x≠-3 U x≠1
1(x-1)+3*(x+3)=x²+5x+2
x²+5x+2-x+1-3x-9=0
x²+x-6=0
x1+x2=-1 U x1*x2=-6
x1=-3 не удов усл
x2=2

oganesbagoyan

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Допустим :
1/(x+3) +3/(x-1) = (x² +5x +2) / (x²+2x -3) ;
( (x-1) +3(x+3) ) / (x+3)(x-1)=(x² +5x +2) / (x²+2x -3) ;
4(x +2) / (x+3)(x-1) = =(x²  +5x +2) / (x+3)(x-1) ;
ОДЗ:   x ≠ - 3 ; x ≠ 1 .
4(x +2) = x²  +5x +2 ;
x² +x - 6 =0 ;
x₁   = - 3   ∉ ОДЗ ;
x₂  = 2.

ответ : 2 .

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