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

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Solution for (2+x)/(3-2x)=-1/2 equation: 


D( x )

3-(2*x) = 0

3-(2*x) = 0

3-(2*x) = 0

3-2*x = 0

3-2*x = 0 // - 3

-2*x = -3 // : -2

x = -3/(-2)

x = 3/2

x in (-oo:3/2) U (3/2:+oo)

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

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

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

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

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

7 = 0

7/(2*(3-2*x)) = 0

7/(2*(3-2*x)) = 0 // * 2*(3-2*x)

7 = 0

x belongs to the empty set

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