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

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


D( x )

x^2-x = 0

x^2-1 = 0

x^2+x = 0

x^2-x = 0

x^2-x = 0

x^2-x = 0

DELTA = (-1)^2-(0*1*4)

DELTA = 1

DELTA > 0

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

x = 1 or x = 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^2+x = 0

x^2+x = 0

x^2+x = 0

DELTA = 1^2-(0*1*4)

DELTA = 1

DELTA > 0

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

x = 0 or x = -1

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

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

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

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

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

x^2-x = 0

x^2-x = 0

x*(x-1) = 0

x-1 = 0 // + 1

x = 1

x*(x-1) = 0

x^2+x = 0

x^2+x = 0

x*(x+1) = 0

x+1 = 0 // - 1

x = -1

x*(x+1) = 0

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

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

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

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

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

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

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

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

1

x = 1

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

1

x-1

3*x^2-4*x-6

3*x^3-7*x^2-2*x+6

x-1

3*x^2-3*x^3

6-4*x^2-2*x

4*x^2-4*x

6-6*x

6*x-6

0

3*x^2-4*x-6 = 0

DELTA = (-4)^2-(-6*3*4)

DELTA = 88

DELTA > 0

x = (88^(1/2)+4)/(2*3) or x = (4-88^(1/2))/(2*3)

x = (2*22^(1/2)+4)/6 or x = (4-2*22^(1/2))/6

x in { (4-2*22^(1/2))/6, (2*22^(1/2)+4)/6, 1} 

(x-((4-2*22^(1/2))/6))*(x-((2*22^(1/2)+4)/6))*(x-1) = 0

((x-((4-2*22^(1/2))/6))*(x-((2*22^(1/2)+4)/6))*(x-1))/(x*(x^2-1)*(x-1)) = 0

((x-((4-2*22^(1/2))/6))*(x-((2*22^(1/2)+4)/6))*(x-1))/(x*(x^2-1)*(x-1)) = 0 // * x*(x^2-1)*(x-1)

(x-((4-2*22^(1/2))/6))*(x-((2*22^(1/2)+4)/6))*(x-1) = 0

( x-((2*22^(1/2)+4)/6) )

x-((2*22^(1/2)+4)/6) = 0 // + (2*22^(1/2)+4)/6

x = (2*22^(1/2)+4)/6

( x-((4-2*22^(1/2))/6) )

x-((4-2*22^(1/2))/6) = 0 // + (4-2*22^(1/2))/6

x = (4-2*22^(1/2))/6

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 1} 

x in { (2*22^(1/2)+4)/6, (4-2*22^(1/2))/6 }

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