1) 2/(x+2) +5x/4(x+2) =13/8 -1/2 ;
(8+5x)/4(x+2) =9/8 ||*8(x+2)
2(8+5x) =9(x+2);
16+10x =9x +18 ;
10x -9x =18 -16;
x =2.
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(x+36)/(x³ -1) -(x+6)/(x-1) +(x²-x+16)/(x²+x+1) =0 || (x³ -1) * * * ОДЗ: x ≠1 * * *
x+36 -(x+6)(x²+x+1) +(x-1)(x²-x+16) =0 ;
x+36 -x³ -x² -x -6x² -6x -6 +x³-x² +16x -x²+x -16 =0;
-9x² +11x +14 =0 ;
9x² -11x -14 =0 ;
D =11² -4*9(-14) =121+504 =625=25²⇒√D =25;
x₁ =(11-25)/(2*9) = -7/9 ;
x₂ =(11+25)/(2*9) =36/18 =2.
ответ : { -7/9 ; 2 }.
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4x²/(x² -1)+(x-2)/(x+1) -(x+2)/(x-1) =0 ;||*(x² -1) * * * ОДЗ: x ≠1 * * *
4x² +(x-2)(x-1) -(x+2)(x+1) =0 ;
4x² +x²-x-2x+2 - (x² +x+2x+2) =0 ;
4x² +x²-x-2x+2 - x² -x-2x-2 =0 ;
4x² -6x=0;
4x(x-1,5) =0 '
x₁=0 ;
x₂=1,5.
ответ : {0 ; 1,5 }.
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(5x²+9)/6 -(4x²-9)/5 =3 ||*30
5(5x²+9) -6(4x²-9) =3*30 ;
25x² +45 -24x²+54 =90 ;
x² +99=90;
x² = -9 нет решения