3)
x/(x+a) +2x/(x-a) =5a²/4(x² -a²) ;
ОДЗ : x≠ ±a .
4x(x-a) +8x(x+a) =5a²;
12x² +4ax -5a² =0 ; D/4 =(2a)² -12*(-5a²) =4a² +60a² =64a² =(8a)² ,
x₁ =(-2a -8a)/12 = -5a/6 ;
x₂ =(-2a+8a)/12 = a/2.
ответ : {- 5a/6 ; a/2}.
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4)
2x/(x+b) -x/(a -x) =b²/4(x² -b²) ;
2x/(x+b) +x/(x - a) =b²/4(x² -b²) ;
ОДЗ : x≠ ±b.
8x(x-b) +4x(x+a) =b² ;
12x² -4bx -b² =0 ; D/4 =(2b)² -12*(-b²) =16b² =(4b)² ,
x₁ =(2b -4b)/12 = -b/6 ;
x₂ =(2b+4b)/12 = b/2.
ответ : {- b/6 ; b/2}.