(7/(x-1))-5=(6/(x^2-1))

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Solution for (7/(x-1))-5=(6/(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)

7/(x-1)-5 = 6/(x^2-1) // - 6/(x^2-1)

7/(x-1)-(6/(x^2-1))-5 = 0

7/(x-1)-6*(x^2-1)^-1-5 = 0

7/(x-1)-6/(x^2-1)-5 = 0

(7*(x^2-1))/((x-1)*(x^2-1))+(-6*(x-1))/((x-1)*(x^2-1))+(-5*(x-1)*(x^2-1))/((x-1)*(x^2-1)) = 0

7*(x^2-1)-6*(x-1)-5*(x-1)*(x^2-1) = 0

7*x^2-5*x^3+5*x^2-6*x+5*x-5-1 = 0

12*x^2-5*x^3-x-6 = 0

12*x^2-5*x^3-x-6 = 0

12*x^2-5*x^3-x-6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

x = 1

12*x^2-5*x^3-x-6 = 0

1

x-1

7*x-5*x^2+6

12*x^2-5*x^3-x-6

x-1

5*x^3-5*x^2

7*x^2-x-6

7*x-7*x^2

6*x-6

6-6*x

0

7*x-5*x^2+6 = 0

DELTA = 7^2-(-5*4*6)

DELTA = 169

DELTA > 0

x = (169^(1/2)-7)/(-5*2) or x = (-169^(1/2)-7)/(-5*2)

x = -3/5 or x = 2

x in { -3/5, 2, 1} 

(x+3/5)*(x-2)*(x-1) = 0

((x+3/5)*(x-2)*(x-1))/((x-1)*(x^2-1)) = 0

((x+3/5)*(x-2)*(x-1))/((x-1)*(x^2-1)) = 0 // * (x-1)*(x^2-1)

(x+3/5)*(x-2)*(x-1) = 0

( x+3/5 )

x+3/5 = 0 // - 3/5

x = -3/5

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 1} 

x in { -3/5, 2 }

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