5/(X-1)+4/(X+1)=6/(X^2-1)

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Solution for 5/(X-1)+4/(X+1)=6/(X^2-1) equation: 


D( X )

X-1 = 0

X^2-1 = 0

X+1 = 0

X-1 = 0

X-1 = 0

X-1 = 0 // + 1

X = 1

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)

5/(X-1)+4/(X+1) = 6/(X^2-1) // - 6/(X^2-1)

5/(X-1)+4/(X+1)-(6/(X^2-1)) = 0

5/(X-1)+4/(X+1)-6*(X^2-1)^-1 = 0

5/(X-1)+4/(X+1)-6/(X^2-1) = 0

(5*(X+1)*(X^2-1))/((X-1)*(X+1)*(X^2-1))+(4*(X-1)*(X^2-1))/((X-1)*(X+1)*(X^2-1))+(-6*(X-1)*(X+1))/((X-1)*(X+1)*(X^2-1)) = 0

5*(X+1)*(X^2-1)+4*(X-1)*(X^2-1)-6*(X-1)*(X+1) = 0

9*X^3+X^2-6*X^2-9*X-1+6 = 0

9*X^3-5*X^2-9*X+5 = 0

9*X^3-5*X^2-9*X+5 = 0

9*X^3-5*X^2-9*X+5 = 0

{ 1, -1, 5, -5 }

1

X = 1

9*X^3-5*X^2-9*X+5 = 0

1

X-1

9*X^2+4*X-5

9*X^3-5*X^2-9*X+5

X-1

9*X^2-9*X^3

4*X^2-9*X+5

4*X-4*X^2

5-5*X

5*X-5

0

9*X^2+4*X-5 = 0

DELTA = 4^2-(-5*4*9)

DELTA = 196

DELTA > 0

X = (196^(1/2)-4)/(2*9) or X = (-196^(1/2)-4)/(2*9)

X = 5/9 or X = -1

X in { -1, 5/9, 1} 

(X+1)*(X-5/9)*(X-1) = 0

((X+1)*(X-5/9)*(X-1))/((X-1)*(X+1)*(X^2-1)) = 0

((X+1)*(X-5/9)*(X-1))/((X-1)*(X+1)*(X^2-1)) = 0 // * (X-1)*(X+1)*(X^2-1)

(X+1)*(X-5/9)*(X-1) = 0

( X+1 )

X+1 = 0 // - 1

X = -1

( X-1 )

X-1 = 0 // + 1

X = 1

( X-5/9 )

X-5/9 = 0 // + 5/9

X = 5/9

X in { -1} 

X in { 1} 

X = 5/9

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