3/(2x+4)=1/(x+2)-2

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Solution for 3/(2x+4)=1/(x+2)-2 equation: 


D( x )

x+2 = 0

2*x+4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

2*x+4 = 0

2*x+4 = 0

2*x+4 = 0 // - 4

2*x = -4 // : 2

x = -4/2

x = -2

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

3/(2*x+4) = 1/(x+2)-2 // - 1/(x+2)-2

3/(2*x+4)-(1/(x+2))+2 = 0

3/(2*x+4)-(x+2)^-1+2 = 0

3/(2*x+4)-1/(x+2)+2 = 0

(3*(x+2))/((2*x+4)*(x+2))+(-1*(2*x+4))/((2*x+4)*(x+2))+(2*(2*x+4)*(x+2))/((2*x+4)*(x+2)) = 0

3*(x+2)-1*(2*x+4)+2*(2*x+4)*(x+2) = 0

4*x^2+x+16*x+2+16 = 0

4*x^2+17*x+18 = 0

4*x^2+17*x+18 = 0

4*x^2+17*x+18 = 0

DELTA = 17^2-(4*4*18)

DELTA = 1

DELTA > 0

x = (1^(1/2)-17)/(2*4) or x = (-1^(1/2)-17)/(2*4)

x = -2 or x = -9/4

(x+9/4)*(x+2) = 0

((x+9/4)*(x+2))/((2*x+4)*(x+2)) = 0

((x+9/4)*(x+2))/((2*x+4)*(x+2)) = 0 // * (2*x+4)*(x+2)

(x+9/4)*(x+2) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x+9/4 )

x+9/4 = 0 // - 9/4

x = -9/4

x in { -2} 

x = -9/4

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