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

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


D( x )

x^2-1 = 0

x^2+4*x+3 = 0

x^2-3+2 = 0

x^2-1 = 0

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

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^2-3+2 = 0

x^2-3+2 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

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

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

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

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

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

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

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

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

3*x^3-4*x^3+2*x^2-16*x^2+5*x-12*x+6 = 0

6-x^3-14*x^2-7*x = 0

6-x^3-14*x^2-7*x = 0

6-x^3-14*x^2-7*x = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

x = 1

6-x^3-14*x^2-7*x = -16

1

-1

x = -1

6-x^3-14*x^2-7*x = 0

-1

x+1

6-x^2-13*x

6-x^3-14*x^2-7*x

x+1

x^3+x^2

6-13*x^2-7*x

13*x^2+13*x

6*x+6

-6*x-6

0

6-x^2-13*x = 0

DELTA = (-13)^2-(-1*4*6)

DELTA = 193

DELTA > 0

x = (193^(1/2)+13)/(-1*2) or x = (13-193^(1/2))/(-1*2)

x = (193^(1/2)+13)/(-2) or x = (13-193^(1/2))/(-2)

x in { (193^(1/2)+13)/(-2), (13-193^(1/2))/(-2), -1} 

(x-((193^(1/2)+13)/(-2)))*(x-((13-193^(1/2))/(-2)))*(x+1) = 0

((x-((193^(1/2)+13)/(-2)))*(x-((13-193^(1/2))/(-2)))*(x+1))/((x+3)*(x+1)*(x^2-1)) = 0

((x-((193^(1/2)+13)/(-2)))*(x-((13-193^(1/2))/(-2)))*(x+1))/((x+3)*(x+1)*(x^2-1)) = 0 // * (x+3)*(x+1)*(x^2-1)

(x-((193^(1/2)+13)/(-2)))*(x-((13-193^(1/2))/(-2)))*(x+1) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-((13-193^(1/2))/(-2)) )

x-((13-193^(1/2))/(-2)) = 0 // + (13-193^(1/2))/(-2)

x = (13-193^(1/2))/(-2)

( x-((193^(1/2)+13)/(-2)) )

x-((193^(1/2)+13)/(-2)) = 0 // + (193^(1/2)+13)/(-2)

x = (193^(1/2)+13)/(-2)

x in { -1} 

x in { (13-193^(1/2))/(-2), (193^(1/2)+13)/(-2) }

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