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

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

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

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

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

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

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

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

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

{ 1, -1, 2, -2, 4, -4 }

1

x = 1

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

1

x-1

4-3*x^2-x

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

x-1

3*x^3-3*x^2

5*x-x^2-4

x^2-x

4*x-4

4-4*x

0

4-3*x^2-x = 0

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

DELTA = 49

DELTA > 0

x = (49^(1/2)+1)/(-3*2) or x = (1-49^(1/2))/(-3*2)

x = -4/3 or x = 1

x in { -4/3, 1, 1} 

(x+4/3)*(x-1)^2 = 0

((x+4/3)*(x-1)^2)/((x-1)*(x^2-1)) = 0

((x+4/3)*(x-1)^2)/((x-1)*(x^2-1)) = 0 // * (x-1)*(x^2-1)

(x+4/3)*(x-1)^2 = 0

( x+4/3 )

x+4/3 = 0 // - 4/3

x = -4/3

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 1} 

x = -4/3

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