(x+7)/(x-1)+(x-1)/(x+1)=4/(x^2-1)

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Solution for (x+7)/(x-1)+(x-1)/(x+1)=4/(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+7)/(x-1)+(x-1)/(x+1) = 4/(x^2-1) // - 4/(x^2-1)

(x+7)/(x-1)+(x-1)/(x+1)-(4/(x^2-1)) = 0

(x+7)/(x-1)+(x-1)/(x+1)-4*(x^2-1)^-1 = 0

(x+7)/(x-1)+(x-1)/(x+1)-4/(x^2-1) = 0

((x+7)*(x+1)*(x^2-1))/((x-1)*(x+1)*(x^2-1))+((x-1)^2*(x^2-1))/((x-1)*(x+1)*(x^2-1))+(-4*(x-1)*(x+1))/((x-1)*(x+1)*(x^2-1)) = 0

(x+7)*(x+1)*(x^2-1)+(x-1)^2*(x^2-1)-4*(x-1)*(x+1) = 0

2*x^4+6*x^3+6*x^2-4*x^2-6*x-8+4 = 0

2*x^4+6*x^3+2*x^2-6*x-4 = 0

2*x^4+6*x^3+2*x^2-6*x-4 = 0

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

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

{ 1, -1, 2, -2 }

1

x = 1

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

1

x-1

x^3+4*x^2+5*x+2

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

x-1

x^3-x^4

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

4*x^2-4*x^3

5*x^2-3*x-2

5*x-5*x^2

2*x-2

2-2*x

0

x^3+4*x^2+5*x+2 = 0

{ 1, -1, 2, -2 }

1

x = 1

x^3+4*x^2+5*x+2 = 12

1

-1

x = -1

x^3+4*x^2+5*x+2 = 0

-1

x+1

x^2+3*x+2

x^3+4*x^2+5*x+2

x+1

-x^3-x^2

3*x^2+5*x+2

-3*x^2-3*x

2*x+2

-2*x-2

0

x^2+3*x+2 = 0

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

DELTA = 1

DELTA > 0

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

x = -1 or x = -2

x in { -2, -1, 1, -1} 

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+2 )

x+2 = 0 // - 2

x = -2

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -1} 

x in { 1} 

x = -2

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