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Norerevi
@Norerevi
July 2022
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Nesh1999
1) (9/x-11)+(11/x-9)=2
(9(x-9)+11(x-11)/(x-11)(x-9))=2
(2(10x-101)/(x-11)(x-9))=2
20x-202=2x^2-40+198
2x^2-60x+400=0
2(x-10)(x-20)=0
x=(10;20) - Ответ
2)(13/x-12)+(12/x-13)=2
(13(x-13)+12(x-12)/(x-12)(x-13))=2
(25x-313/(x-12)(x-13))=2
25x-313=2x^2-50x+312
2x^2-75x+625=0
(2x-25)(x-25)=0
x=(25/2 ; 25) - Ответ
3)(8/x-3)+(3/x-8)=2
(8(x-8)+3(x-3)/(x-3)(x-8))=2
11x-73/(x-3)(x-8)=2
11x-73=2x^2-22x+48
2x^2-33x+121=0
(2x-11)(x-11)=0
x=(11/2 ; 11) - Ответ
4)(10/x-4)+(4/x-10)=2
(10(x-10)+4(x-4)/(x-10)(x-4))=2
(2(7x-58)/(x-10)(x-4))=2
14x-116=2x^2-28x+60
2x^2-42x+196=0
2(x-7)(x-14)=0
(x-7)(x-14)=0
x=(7;14) - Ответ
5)(x-6)/(x-9)=2 - Умножаем все на (x-9)
x-6=2(x-9)
x-6=2x-18
-x=-12 (*(-1))
x=12 - Ответ
6)(x-5)(x-9)=5
x-5=5x-45
-4x=-40
x=10 - Ответ
7)x-5/x-15=-1
x-5=-x+15
x-5+x=15
2x-5=15
2x=20
x=10 - Ответ
4 votes
Thanks 1
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Answers & Comments
(9(x-9)+11(x-11)/(x-11)(x-9))=2
(2(10x-101)/(x-11)(x-9))=2
20x-202=2x^2-40+198
2x^2-60x+400=0
2(x-10)(x-20)=0
x=(10;20) - Ответ
2)(13/x-12)+(12/x-13)=2
(13(x-13)+12(x-12)/(x-12)(x-13))=2
(25x-313/(x-12)(x-13))=2
25x-313=2x^2-50x+312
2x^2-75x+625=0
(2x-25)(x-25)=0
x=(25/2 ; 25) - Ответ
3)(8/x-3)+(3/x-8)=2
(8(x-8)+3(x-3)/(x-3)(x-8))=2
11x-73/(x-3)(x-8)=2
11x-73=2x^2-22x+48
2x^2-33x+121=0
(2x-11)(x-11)=0
x=(11/2 ; 11) - Ответ
4)(10/x-4)+(4/x-10)=2
(10(x-10)+4(x-4)/(x-10)(x-4))=2
(2(7x-58)/(x-10)(x-4))=2
14x-116=2x^2-28x+60
2x^2-42x+196=0
2(x-7)(x-14)=0
(x-7)(x-14)=0
x=(7;14) - Ответ
5)(x-6)/(x-9)=2 - Умножаем все на (x-9)
x-6=2(x-9)
x-6=2x-18
-x=-12 (*(-1))
x=12 - Ответ
6)(x-5)(x-9)=5
x-5=5x-45
-4x=-40
x=10 - Ответ
7)x-5/x-15=-1
x-5=-x+15
x-5+x=15
2x-5=15
2x=20
x=10 - Ответ