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aregumminn1365
@aregumminn1365
July 2022
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Решите уравнение: [tex] \frac{2}{x-2} - \frac{3x+1}{x+2}= \frac{2x+3}{ x^{2}-4 } [/tex]
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LyubaAlexandorovna
ОДЗ х не равен 2, -2
Запишем x^2-4=(x-2)*(x+2) и приведём к общему множителю
(2*(x+2)-(3*x+1)*(x-2)-2*x-3)/(x+2)*(x-2)=0
2*x+4-3*x^2+5*x+2-2*x-3=0
-3*x^2+5*x+3=0 (*-1)
3*x^2-5*x-3=0
x1,2=(5±√(25+36))/6=(5±61)/6
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Запишем x^2-4=(x-2)*(x+2) и приведём к общему множителю
(2*(x+2)-(3*x+1)*(x-2)-2*x-3)/(x+2)*(x-2)=0
2*x+4-3*x^2+5*x+2-2*x-3=0
-3*x^2+5*x+3=0 (*-1)
3*x^2-5*x-3=0
x1,2=(5±√(25+36))/6=(5±61)/6