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1234554321c
@1234554321c
August 2022
2
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решите уравнение
1/х+3+3/х-1=х^2+5х+2/х^2+2x-3
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sedinalana
Verified answer
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
6 votes
Thanks 6
oganesbagoyan
Verified answer
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
.
:
4 votes
Thanks 2
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Answers & Comments
Verified answer
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
Verified answer
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 .
: