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

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


D( x )

x^2-1 = 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 in (-oo:-1) U (-1:1) U (1:+oo)

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

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

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

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

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

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

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

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

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

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

{ 1, -1, 3, -3 }

1

x = 1

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

1

x-1

x^2+2*x-3

x^3+x^2-5*x+3

x-1

x^2-x^3

2*x^2-5*x+3

2*x-2*x^2

3-3*x

3*x-3

0

x^2+2*x-3 = 0

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

DELTA = 16

DELTA > 0

x = (16^(1/2)-2)/(1*2) or x = (-16^(1/2)-2)/(1*2)

x = 1 or x = -3

x in { -3, 1, 1}

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

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

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

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

( x+3 )

x+3 = 0 // - 3

x = -3

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 1}

x = -3

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