Question

solve the equaion: 3x+2div x-2+ 1div x= -2div x ^{2}-2x

Answer 1

\[3x+2\div x-2+ 1\div x= -2\div x ^{2}-2x\]
considering there are brackets (I don't see any),
\[(3x+2)/(x-2) + 1/x = -2/(x ^{2}-2x)\]
reduce to a common denominator
\[(3x ^{2}+3x-2)/(x ^{2}-2x) = -2/(x ^{2}-2x)\]
multiply their denominator to each side
and \[3x ^{2}+3x-2=-2\] is what you get.
add 2 to each side \[3x ^{2}+3x=0\]
divide by 3, and \[x(x+1)=0\] is what is left.
\[\therefore x=0,(-1)\]

Answer 2

3x+2 1 -2
---- + ---- = ---------
x-2 x x*(2) - 2x

3x+2 1 -2
----- + ---- = -------
x-2 x x(x-2)

x(3x+2) + x-2 = -2
3x*2 +2x +x -2= -2
3x*2+3x=0
3x(x+1)=0

3x=0 --- x=0
x+1=0 -- x= -1

Answer 3

x=0 is not solution of this equation