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

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


D( x )

x^2-1 = 0

x+1 = 0

x-1 = 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+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

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

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

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

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

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

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

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

x^4-3*x^2+2 = 0

x^4-3*x^2+2 = 0

x^4-3*x^2+2 = 0

{ 1, -1, 2, -2 }

1

x = 1

x^4-3*x^2+2 = 0

1

x-1

x^3+x^2-2*x-2

x^4-3*x^2+2

x-1

x^3-x^4

x^3-3*x^2+2

x^2-x^3

2-2*x^2

2*x^2-2*x

2-2*x

2*x-2

0

x^3+x^2-2*x-2 = 0

{ 1, -1, 2, -2 }

1

x = 1

x^3+x^2-2*x-2 = -2

1

-1

x = -1

x^3+x^2-2*x-2 = 0

-1

x+1

x^2-2

x^3+x^2-2*x-2

x+1

-x^3-x^2

-2*x-2

2*x+2

0

x^2-2 = 0

DELTA = 0^2-(-2*1*4)

DELTA = 8

DELTA > 0

x = (8^(1/2)+0)/(1*2) or x = (0-8^(1/2))/(1*2)

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

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

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+2^(1/2) )

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

x = -2^(1/2)

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2^(1/2) )

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

x = 2^(1/2)

x in { -1} 

x in { 1} 

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

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