1) x÷(3+x) + 4x+6÷(x^2+4x+3)=0 2) a) 2x+1/(x-3) ≤ 1 b) (x-2)(x+5)÷(x-1)^2

Question

1) x÷(3+x) + 4x+6÷(x^2+4x+3)=0
2)
a) 2x+1/(x-3) ≤ 1
b) (x-2)(x+5)÷(x-1)^2

Answer 1

x^3 - 3x^2 - 4x = 0,

x(x^2-3x-4)=0,

x1=0,

x^2-3x-4=0,

x2=-1, x3=4;

 

(2x - 1)^4 - x^2 = 0,

((2x-1)^2)^2-x^2=0,

((2x-1)^2-x)((2x-1)^2+x)=0,

(2x-1)^2-x=0,

4x^2-5x+1=0,

D=9,

x1=1/4, x2=1;

(2x-1)^2+x=0,

4x^2-3x+1=0,

D=-7<0; нет решений</p>

 

x^3 - 3x^2 - x +3 = 0,

x^2(x-3)-(x-3)=0,

(x-3)(x^2-1)=0,

x-3=0, x1=3;

x^2-1=0, x^2=1, x2=-1, x3=1