a)
\frac{1-2x}{x}=3x , x\ne 0 , D=R \ {0}
1-2x=3x^2
-3x^2-2x+1=0|*(-1)
3x^2+2x-1=0
3x^2+3x-x-1=0
3x(x+1)-(x+1)=0
(x+1)(3x-1)=0
x+1=0 \vee 3x-1=0
x=-1\vee 3x=1
x_1=-1 , x_2=\frac{1}{3}
b)
\frac{1}{2x}+\frac{7}{4x}=x , 2x\ne 0 i 4x\ne 0 , x \ne 0 , D=R \ {0}
\frac{2+7}{4x}=x
\frac{9}{4x}=x
9=4x^2|:4
x^2=\frac{9}{4}
x_1=-\frac{3}{2} , x_2=\frac{3}{2}
c)
2x+\frac{3-x}{x}=4 , x\ne 0 D=R \ {0}
\frac{2x^2+3-x}{x}=4
2x^2+3-x=4x
2x^2+3-x-4x=0
2x^2-5x+3=0
2x^2-2x-3x+3=0
2x(x-1)-3(x-1)=0
(x-1)(2x-3)=0
x-1=0\vee 2x-3=0
x=1\vee 2x=3
x_1=1 , x_2=\frac{3}{2}
\vee znaczy “lub”