d)
\frac{2x-2}{x+2}=\frac{x}{x-1}
x\ne2 , x\ne 1
(2x-2)(x-1)=x(x+2)
2x^2-2x-2x+2=x^2+2x
2x^2-4x+2-x^2-2x=0
x^2-6x+2=0
a=1, b=-6, c=2
\Delta=36-4*2=28
\sqrt\Delta=\sqrt{4*7}=2\sqrt7
x_1=\frac{6-2\sqrt7}{2}=\frac{2(3-\sqrt7)}{2}=3-\sqrt7
x_2=\frac{6+2\sqrt7}{2}=\frac{2(3+\sqrt7}{2}=3+\sqrt7
e)
\frac{6x-4}{2-3x}=-2x
-3x\ne-2 => x\ne\frac{2}{3}
\frac{-2(2-3x)}{2-3x}=-2x
-2=-2x |:(-2)
1=x
x=1
f)
6x+1=\frac{2}{x}
x\ne0
6x+1-\frac{2}{x}=0
\frac{(6x+1)*x-2}{x}=0
\frac{6x^2+x-2}{x}=0
6x^2+x-2=0
a=6, b=1, c=-2
\Delta=1-4*6*(-2)=49
\sqrt\Delta=7
x_1=\frac{-1-7}{2*6}=\frac{-8}{12}=-\frac{2}{3}
x_2=\frac{-1+7}{12}=\frac{6}{12}=\frac{1}{2}