(x/(x+1))+((3x+5)/(x^2+4x+3))=2/(x+3)

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Solution for (x/(x+1))+((3x+5)/(x^2+4x+3))=2/(x+3) equation: 


D( x )

x^2+4*x+3 = 0

x+1 = 0

x+3 = 0

x^2+4*x+3 = 0

x^2+4*x+3 = 0

x^2+4*x+3 = 0

DELTA = 4^2-(1*3*4)

DELTA = 4

DELTA > 0

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

x = -1 or x = -3

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:-1) U (-1:+oo)

x/(x+1)+(3*x+5)/(x^2+4*x+3) = 2/(x+3) // - 2/(x+3)

x/(x+1)+(3*x+5)/(x^2+4*x+3)-(2/(x+3)) = 0

x/(x+1)+(3*x+5)/(x^2+4*x+3)-2*(x+3)^-1 = 0

x/(x+1)+(3*x+5)/(x^2+4*x+3)-2/(x+3) = 0

x^2+4*x+3 = 0

x^2+4*x+3 = 0

x^2+4*x+3 = 0

DELTA = 4^2-(1*3*4)

DELTA = 4

DELTA > 0

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

x = -1 or x = -3

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

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

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

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

x^2+6*x-2*x-2+5 = 0

x^2+4*x+3 = 0

x^2+4*x+3 = 0

x^2+4*x+3 = 0

DELTA = 4^2-(1*3*4)

DELTA = 4

DELTA > 0

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

x = -1 or x = -3

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+3 )

x+3 = 0 // - 3

x = -3

x in { -1} 

x in { -3} 

x belongs to the empty set

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