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

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


D( x )

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

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

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

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

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

2*x^2+x-3 = 0

2*x^2+x-3 = 0

2*x^2+x-3 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(2*2) or x = (-25^(1/2)-1)/(2*2)

x = 1 or x = -3/2

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

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

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

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

( x+3/2 )

x+3/2 = 0 // - 3/2

x = -3/2

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 1} 

x = -3/2

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