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polina4499
@polina4499
July 2022
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(24/(x^2-2x))-(12/(x^2-x))=x^2-x
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BOR48
24/(x²-2x) -12/(x²-x) = x²-x ;
24/x(x-2) -12/x(x-1) = x(x-1) ;
* * * ОДЗ: x ≠ 0 ;1; 2 * * *
(
24(x-1) -12(x-2))/x(x-1)(x-2) = x(x-1) ;
(12x)/x(x-1)(x-2) = x(x-1) ;
12 /(x-1)(x-2) = x(x-1) ;
(x-1)(x-2) * x(x-1) =12 ;
(x-1)²*x(x-2) =12 ;
(x-1)² ((x-1)² -1) =12 ;
* * * t =(x-1)² ≥0 ; ясно x=1 не решение * * *
t² -t -12=0 ;
t₁ = -3 <0 →не решение ;
t₂ =4 ⇒( x-1)² =4⇒ [ x-1 =-2 ; x-1 =2⇔[ x= -1 ; x=3.
ответ : {-1 ; 3} .
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polina4499
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Answers & Comments
24/x(x-2) -12/x(x-1) = x(x-1) ;
* * * ОДЗ: x ≠ 0 ;1; 2 * * *
(24(x-1) -12(x-2))/x(x-1)(x-2) = x(x-1) ;
(12x)/x(x-1)(x-2) = x(x-1) ;
12 /(x-1)(x-2) = x(x-1) ;
(x-1)(x-2) * x(x-1) =12 ;
(x-1)²*x(x-2) =12 ;
(x-1)² ((x-1)² -1) =12 ;
* * * t =(x-1)² ≥0 ; ясно x=1 не решение * * *
t² -t -12=0 ;
t₁ = -3 <0 →не решение ;
t₂ =4 ⇒( x-1)² =4⇒ [ x-1 =-2 ; x-1 =2⇔[ x= -1 ; x=3.
ответ : {-1 ; 3} .