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

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


D( x )

x = 0

x/(x-1) <= 0

x^2-1 <= 0

(x+1)/x <= 0

x-1 = 0

x = 0

x = 0

x/(x-1) <= 0

x/(x-1) <= 0

( x-1 )

x-1 <= 0 // + 1

x <= 1

( x )

x+0 <= 0 // - 0

x <= 0

(-oo:0)(0:1)(1:+oo)x-1--+x-++

x^2-1 <= 0

x^2-1 <= 0

1*x^2 <= 1

1*x^2 <= 1 // : 1

x^2 <= 1/1

x^2 <= 1

x^2 <= 1 // ^ 1/2

abs(x) <= 1

x in <-1:1>

(x+1)/x <= 0

(x+1)/x <= 0

( x+1 )

x+1 <= 0 // - 1

x <= -1

( x )

x+0 <= 0 // - 0

x <= 0

(-oo:-1)(-1:0)(0:+oo)x+1-++x--+

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

x-x^2+2 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)-1)/(-1*2) or x = (-9^(1/2)-1)/(-1*2)

x = -1 or x = 2

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x-2 )

x-2 = 0 // + 2

x = 2

( x^2 )

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { -1} 

x in { 0} 

x = 2

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