(x+3)/(x^2+5x+6)=(2)/(2x+6)-(3)/(x+2)

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Solution for (x+3)/(x^2+5x+6)=(2)/(2x+6)-(3)/(x+2) equation: 


D( x )

x^2+5*x+6 = 0

x+2 = 0

2*x+6 = 0

x^2+5*x+6 = 0

x^2+5*x+6 = 0

x^2+5*x+6 = 0

DELTA = 5^2-(1*4*6)

DELTA = 1

DELTA > 0

x = (1^(1/2)-5)/(1*2) or x = (-1^(1/2)-5)/(1*2)

x = -2 or x = -3

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

2*x+6 = 0

2*x+6 = 0

2*x+6 = 0 // - 6

2*x = -6 // : 2

x = -6/2

x = -3

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

(x+3)/(x^2+5*x+6) = 2/(2*x+6)-(3/(x+2)) // - 2/(2*x+6)-(3/(x+2))

(x+3)/(x^2+5*x+6)-(2/(2*x+6))+3/(x+2) = 0

(x+3)/(x^2+5*x+6)-2*(2*x+6)^-1+3/(x+2) = 0

(x+3)/(x^2+5*x+6)-2/(2*x+6)+3/(x+2) = 0

x^2+5*x+6 = 0

x^2+5*x+6 = 0

x^2+5*x+6 = 0

DELTA = 5^2-(1*4*6)

DELTA = 1

DELTA > 0

x = (1^(1/2)-5)/(1*2) or x = (-1^(1/2)-5)/(1*2)

x = -2 or x = -3

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

(x+3)/((x+3)*(x+2))-2/(2*x+6)+3/(x+2) = 0

((x+3)*(2*x+6))/((x+3)*(x+2)*(2*x+6))+(-2*(x+3)*(x+2))/((x+3)*(x+2)*(2*x+6))+(3*(x+3)*(2*x+6))/((x+3)*(x+2)*(2*x+6)) = 0

(x+3)*(2*x+6)-2*(x+3)*(x+2)+3*(x+3)*(2*x+6) = 0

6*x^2+2*x+36*x+6+54 = 0

6*x^2+38*x+60 = 0

6*x^2+38*x+60 = 0

2*(3*x^2+19*x+30) = 0

3*x^2+19*x+30 = 0

DELTA = 19^2-(3*4*30)

DELTA = 1

DELTA > 0

x = (1^(1/2)-19)/(2*3) or x = (-1^(1/2)-19)/(2*3)

x = -3 or x = -10/3

2*(x+10/3)*(x+3) = 0

(2*(x+10/3)*(x+3))/((x+3)*(x+2)*(2*x+6)) = 0

(2*(x+10/3)*(x+3))/((x+3)*(x+2)*(2*x+6)) = 0 // * (x+3)*(x+2)*(2*x+6)

2*(x+10/3)*(x+3) = 0

( x+10/3 )

x+10/3 = 0 // - 10/3

x = -10/3

( x+3 )

x+3 = 0 // - 3

x = -3

x in { -3} 

x = -10/3

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