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

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Solution for 6/(x+1)-5/(x-1)=3x/(x^2-1) equation:


D( x )

x^2-1 = 0

x+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-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

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

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

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

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

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

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

x^3-3*x^3-11*x^2-x+3*x+11 = 0

2*x-2*x^3-11*x^2+11 = 0

2*x-2*x^3-11*x^2+11 = 0

2*x-2*x^3-11*x^2+11

11*(1-x^2)-2*x^3+2*x

2*x*(1-x^2)+11*(1-x^2)

(2*x+11)*(1-x^2)

((2*x+11)*(1-x^2))/((x+1)*(x-1)*(x^2-1)) = 0

((2*x+11)*(1-x^2))/((x+1)*(x-1)*(x^2-1)) = 0 // * (x+1)*(x-1)*(x^2-1)

(2*x+11)*(1-x^2) = 0

( 1-x^2 )

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

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

( 2*x+11 )

2*x+11 = 0 // - 11

2*x = -11 // : 2

x = -11/2

x in { 1}

x in { -1}

x = -11/2

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